Zoom lens system

ABSTRACT

A zoom lens system in which a movement locus of a focusing lens unit is defined by synthesizing a focus cam and a zoom compensation cam so as to achieve an in-focus state by a substantially constant amount of rotation for an identical object distance independently of a zooming state. In zooming, an amount of movement of the focusing lens unit is defined by a combination of the focus cam and the zoom compensation cam. An amount of movement of a non-focusing lens unit is defined by a combination of a zoom cam and the zoom compensation cam. In focusing, the amount of movement of the focusing lens unit is defined by the focus cam. The zoom lens system satisfies specified formulas so that the number of data of specific coefficients required for auto-focusing can be reduced, and an error upon calculation of the lens driving amount of the focusing lens unit using stored specific coefficients in correspondence with a detected defocus amount can be reduced.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a zoom lens and, more particularly, toa zoom lens attached to a so-called auto-focusing camera, video camera,or the like, which has a focus detection device, and moves a focusinglens unit in a photographing optical system in accordance with thedetected defocus amount.

2. Related Background Art

In recent years, along with the wide spread use of auto-focusingcameras, various focusing systems such as a so-called inner focusingsystem, rear focusing system, and the like have been examined to make afocusing lens of a zoom lens compact.

However, in general, when a focusing system other than a so-called frontfocusing system is adopted, the lens driving amount for focusing changesupon a change in focal length. To solve this problem, Japanese PatentApplication Laid-Open Nos. 4-293008 and 5-142475 assigned to the sameassignee as the present invention proposed a method of realizing aso-called manual focusing operation in a zoom lens having a plurality oflens units including a focusing lens unit having both zooming andfocusing functions. In this method, when a predetermined movement locusfor zooming is expressed by the amount of movement of the lens units inthe direction of the optical axis and the angle of rotation of arotatable lens barrel, the movement locus of the focusing lens unit isdefined by synthesizing a focus cam and a zoom compensation cam. Withthis arrangement, even when the amount of movement for focusing alongthe optical axis changes depending on the zooming state, the angle ofrotation of the rotatable lens barrel for focusing is left unchanged,thus achieving a manual focusing operation.

However, when the above-mentioned zoom lens is applied to anauto-focusing camera system, which comprises focus detection means,storage means for storing the conversion coefficient γ and thecorrection coefficient ε used for calculating the lens driving amount Δxfor focusing the focusing lens unit on the basis of the detected defocusamount ΔBf of a photographing optical system, and calculation means forcalculating the lens driving amount Δx for focusing using the defocusamount ΔBf, the conversion coefficient γ, and the correction coefficientε, problems associated with the storage capacity, calculation error, andthe like are posed.

As in Japanese Patent Application Laid-Open Nos. 4-293008 and 5-142475above, in a zoom lens disclosed in Japanese Patent Application Laid-OpenNos. 57-37307, 57-37308, 63-49715, 63-314511, 3-144411, 3-235908,3-249717, 4-184402, 4-184403, 4-184404, 4-184405, 4-184406, 4-186207,4-186208, 7-110446, and the like, in each of which the movement locus ofthe focusing lens unit is defined by synthesizing a focus cam and a zoomcompensation cam, the above-mentioned problems concerning the storagecapacity, calculation error, and the like have not been examined,either.

Furthermore, in a zoom lens disclosed in Japanese Patent ApplicationLaid-Open Nos. 57-4018, 58-137812, 58-137814, 58-144808, 58-149014,58-150925, and the like, each of which utilizes only a focus cam, theproblems of the storage capacity, calculation error, and the like havenot been examined, either.

On the other hand, as in Japanese Patent Application Laid-Open Nos.63-163808, 1-154014, and the like assigned to the same assignee as thepresent invention, in a zoom lens disclosed in Japanese PatentApplication Laid-Open Nos. 64-35515, 64-35516, 4-140704, and the like,each of which commonly uses a single cam as both a focus cam and a zoomcam, the above-mentioned problems of the storage capacity, calculationerror, and the like have not been examined, either. In addition, thezoom lens disclosed in these references has a basic structure differentfrom that of the present invention since it does not require any zoomcompensation cam, and does not take a so-called flexible manual focusingoperation into account, which has been examined in Japanese PatentApplication Laid-Open Nos. 4-293008, 5-142475, and the like.

A zoom lens disclosed in Japanese Patent Application Laid-Open Nos.2-256011 and 3-101707 which have been assigned to the same assignee asthe present invention, and Japanese Patent Application Laid-Open No.7-120662 which discloses a technical content similar to those disclosedin the above Japanese Patent Application Laid-Open Nos. 2-256011 and3-101707, has a basic structure different from that of the presentinvention since it realizes zooming by a relative movement, in thedirection of rotation of a lens barrel, between a focus cam and a zoomcam, and focusing by a relative movement in the direction of the opticalaxis, and does not examine an auto-focusing operation at all.

Similarly, in Japanese Patent Application Laid-Open No. 7-5362, a zoomlens disclosed therein has a basic structure different from that of thepresent invention since the amount of movement for focusing is to bedefined by synthesizing -two kinds of cams without using a focus camdirectly, and the above-mentioned problems concerning the storagecapacity, calculation error, and the like have not been examined.

Furthermore, Japanese Patent Application Laid-Open Nos. 61-77027,1-232313, and the like disclose a lens system having a focus cam so asto realize an accurate auto-focusing operation with a small calculationerror. However, these references relate to a single-focus lens having nozooming function, and cannot be applied to a focus cam required toachieve a so-called manual focusing operation in a zoom lens in whichthe amount of movement in the direction of the optical axis for focusingchanges depending on the zooming state.

The principle of the auto-focus operation will be briefly describedbelow.

An auto-focusing system disclosed in Japanese Patent ApplicationLaid-Open Nos. 62-78519, 62-170924, 1-131507, 1-131508, 1-131509,3-228006, and the like, comprises focus detection means, calculationmeans for calculating the lens driving amount for focusing, and storagemeans for storing specific constants used in calculations. In thissystem, the focus detection means detects the defocus amount ΔBf betweenthe imaging position of an actual object by the photographing opticalsystem and a predetermined imaging point position, and the calculationmeans for calculating the lens driving amount for focusing calculatesthe lens driving amount Δx for focusing on the basis of the detecteddefocus amount ΔBf of the photographing optical system, thus achievingan auto-focusing operation.

If the relationship between the lens driving amount Δx for focusing andthe defocus amount ΔBf is expressed using a conversion coefficient Kassociated with focusing as follows:

    Δx=ΔBf/K

then, the lens driving amount Ax can be calculated by setting theconversion coefficient K.

However, as described in Japanese Patent Application Laid-Open No.62-170924, the conversion coefficient K changes in correspondence notonly with the focal length but also with the object position and lensarrangement.

Therefore, as described in Japanese Patent Application Laid-Open Nos.62-78519, 62-170924, and the like, using the conversion coefficient γdefined as the ratio (sensitivity) of the amount of infinitesimalmovement of the imaging plane with respect to the amount ofinfinitesimal movement of the focusing lens unit in the vicinity of apredetermined in-focus point, and the correction coefficient ε forcorrecting the conversion coefficient in accordance with the defocusamount ΔBf, the conversion coefficient K is calculated by the followingformulas:

    K=γ+ε.f(ΔBf)

    K=γ+ε.ΔBf.sup.2 in Japanese Patent Application Laid-Open No. 62-78519

    K=γ(1+ε.ΔBf) in Japanese Patent Application Laid-Open No. 62-170924

and thereafter, the lens driving amount Δx is calculated based on theconversion coefficient K. (Of course, the lens driving amount Δx forfocusing may be directly calculated from the defocus amount ΔBf usingthe conversion coefficient y and the correction coefficient ε.)Furthermore, in a photographing system having a zooming optical system,since the values of the conversion coefficient γ and the correctioncoefficient ε change depending on the lens arrangement, a plurality ofpairs of data of the conversion coefficient γ and the correctioncoefficient ε are stored in the storage means in units of a plurality ofdivided zoom ranges and focus ranges, as described in Japanese PatentApplication Laid-Open No. 3-228006.

In other words, in the photographing system having the zooming opticalsystem, the focus detection means detects the defocus amount ΔBf causedby the zooming optical system, and values of the conversion coefficientγ and the correction coefficient ε corresponding to the zoom and focuspositions respectively detected by zoom and focus position detectionmeans are read out from the storage means. The calculation means forcalculating the lens driving amount for focusing calculates the lensdriving amount Δx for focusing using the defocus amount ΔBf, theconversion coefficient γ, and the correction coefficient ε, and drivingmeans drives a lens by the calculated lens driving amount Δx forfocusing, thus achieving a focusing operation.

However, in a normal focusing mechanism using a helicoid mechanism or acam mechanism, the lens driving amount for focusing must be describednot as a lens driving amount Δx in the direction of the optical axis butas a lens driving amount Δa in the direction of rotation.

Therefore, when the relationship between the lens driving amount Δx andthe defocus amount ΔBf in the direction of the optical axis is convertedinto the relationship between the lens driving amount Δa and the defocusamount ΔBf in the direction of rotation using a conversion coefficientK_(a) associated with the direction of rotation, we have:

    Δa=ΔBf/K.sub.a

If conversion coefficient K associated with the direction of the opticalaxis is newly defined as K_(x), the conversion coefficient K_(a)associated with the direction of rotation is expressed using aconversion coefficient Φ between the lens driving amount Δx in thedirection of the optical axis and the lens driving amount Δa in thedirection of rotation as follows:

    K.sub.a =K.sub.x.Φ

Thus, the formula in Japanese Patent Application Laid-Open No. 62-170924is modified to a formula associated with the conversion coefficientK_(a) in the direction of rotation as follows:

    K.sub.a =Φε(1+ε.ΔBf)

If Δx and Δa have a linear relationship therebetween like in a helicoidmechanism, Φ becomes a constant. However, when a cam mechanism is used,the conversion coefficient Φ changes depending on the cam shape. Theconversion coefficient Φ can be replaced by a slope (dx/da) defined bythe cam shape as follows:

    K.sub.a =γ.(dx/da)(1+ε.ΔBf)

The conversion coefficient γ and the correction coefficient ε in aninner focusing type zoom lens disclosed in Japanese Patent ApplicationLaid-Open Nos. 4-293008, 5-142475, and the like will be examined below.

When a zoom lens system is constituted by n lens units, and its k-thlens unit is used as the focusing lens unit, if the ratio of the amountdBf of infinitesimal movement of the imaging plane to the amount dx ofinfinitesimal movement, in the direction of the optical axis, of thefocusing lens unit, i.e., the conversion coefficient ε (dBf/dx: thesensitivity associated with movement in the direction of the opticalaxis) is defined as a new conversion coefficient γ_(x) associated withthe amount x of movement in the direction of the optical axis, theconversion coefficient γ_(x) can be expressed using the imagingmagnifications β of the respective lens units as follows:

    γ.sub.x =(1-β.sub.k.sup.2)β.sub.k+1.sup.2 β.sub.k+2.sup.2 . . . β.sub.n.sup.2

Therefore, the rate of change, from the infinity in-focus value (γ_(xO))to the closest in-focus value (γ_(xR)), of the conversion coefficientγ_(x) associated with the amount x of movement in the direction of theoptical axis can be expressed using the imaging magnifications β_(Ok)and β_(Rk) of the focusing lens unit at the infinity and closestin-focus points as follows:

    γ.sub.xR /γ.sub.xO =(1-β.sub.Rk.sup.2)/(1-β.sub.Ok.sup.2)

Furthermore, if the ratio of the amount dBf of infinitesimal movement ofthe imaging plane to the angle da of infinitesimal rotation of thefocusing lens unit (dBf/da: the sensitivity associated with movement inthe direction of rotation) is defined as a new conversion coefficientγ_(a) associated with the angle a of rotation of a rotatable lensbarrel, the conversion coefficient γ_(a) associated with the angle a ofrotation of the rotatable lens barrel can be expressed by:

    γ.sub.a =γ.sub.x.(dx/da)

where dx/da is the slope of the focus cam.

Therefore, the rate of change, from the infinity in-focus value (γ_(aO))to the closest in-focus value (γ_(aR)), of the conversion coefficientγ_(a) associated with the angle a of rotation of the rotatable lensbarrel can be expressed using slopes (dx/da)_(O) and (dx/da)_(R) at theinfinity and closest corresponding positions on the focus cam asfollows:

    γ.sub.aR /γ.sub.aO =(γ.sub.xR /γ.sub.xO).((dx/da).sub.R /(dx/da).sub.O)

The rate of change of the conversion coefficient γ_(x) with respect tothe amount x of movement in the direction of the optical axis and therate of change of the conversion coefficient γ_(a) with respect to theangle a of rotation of the rotatable lens barrel will be examined belowin association with an embodiment of Japanese Patent Applicationlaid-Open No. 5-142475. Note that the amount of rotation for zoomingfrom the wide-angle end to the telephoto end and the amount of rotationfor focusing are respectively re-set to be 10.0 for the purpose of acomparison with an embodiment of the present invention.

Table 1 below summarizes various paraxial data of an optical system anddata for defining the shape of the focus cam corresponding to theembodiment of Japanese Patent Application Laid-Open No. 5-142475.

The upper table in Table 1 summarizes the focal length data andprincipal point interval data of the respective lens units of theoptical system corresponding to the embodiment of Japanese PatentApplication Laid-Open No. 5-142475. In this table, F1, F2, F3, and F4are respectively the focal lengths of first, second, third and fourthlens units, and D1, D2, D3, and D4 are respectively the principal pointinterval between the first and second lens units, the principal pointinterval between the second and third lens units, the principal pointinterval between the third and fourth lens units, and the principalpoint interval between the fourth lens unit and a predetermined imagingplane in six zooming states (focal lengths F=36.0 (1-POS), 50.0 (2-POS),60.0 (3-POS), 70.0 (4-POS), 85.0 (5-POS), and 103.0 mm (6-POS)).

The middle table in Table 1 summarizes spline sample point data when theshape of the focus cam in the second lens unit which is used forfocusing is expressed by a spline function associated with the angle aof rotation of the rotatable lens barrel and the amount x of movement inthe direction of the optical axis (complying with "Numerical Analysisand FORTRAN", MARUZEN, "Spline Function and Its Applications", KyoikuShuppan, and the like). In this middle table, (1), (2), (3), and (4)correspond to the first, second, third, and fourth lens units,respectively.

Furthermore, the lower table in Table 1 summarizes the infinity focusingpositions (infinity corresponding positions) at the respective focallengths (F=36.0, 50.0, 60.0, 70.0, 85.0, and 103.0 mm), and the amountsof rotation (amounts of rotation for focusing) upon focusing torespective photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.0, and 0.85m) using the focus cam. Since both the amount of rotation for zoomingfrom the wide-angle end (F=36.0) to the telephoto end (F=103.0) and theamount of rotation for focusing from the infinity in-focus position tothe closest in-focus position (R=0.85 m) are 10.0, the rotation amountratio (a_(F) /a_(Z)) of the amount of rotation for focusing to theamount of rotation for zooming is 1.0.

                                      TABLE 1                                     __________________________________________________________________________    Data of Embodiment of Japanese Patent Application Laid-Open                   No. 5-142475 (Rotation Amount Ratio: a.sub.F /a.sub.Z = 1.0)                  __________________________________________________________________________    Focal lengths and Principal Point Intervals of Lens Units of Embodiment       of                                                                            Japanese Patent Application Laid-Open No. 5-142475                                       1-POS                                                                             2-POS                                                                              3-POS                                                                             4-POS                                                                              5-POS                                                                             6-POS                                        __________________________________________________________________________            F  36.0000                                                                           50.0000                                                                            60.0000                                                                           70.0000                                                                            85.0000                                                                           103.0000                                     F1 71.3528                                                                            D1 10.0000                                                                           16.9506                                                                            20.8432                                                                           24.0040                                                                            27.6859                                                                           31.0684                                      F2 -16.8076                                                                           D2 18.0119                                                                           13.8825                                                                            11.8221                                                                           10.1086                                                                             7.9077                                                                           5.6236                                       F3 37.3219                                                                            D3 13.2200                                                                           12.3744                                                                            11.9702                                                                           11.6986                                                                            11.3811                                                                           11.3103                                      F4 61.7098                                                                            D4 53.2211                                                                           59.4228                                                                            62.5744                                                                           65.1172                                                                            68.2854                                                                           71.2371                                      __________________________________________________________________________    Focus Cam Shape (Spline Interpolation) Corresponding to                       Embodiment of Japanese Patent Application Laid-Open No. 5-142475                   ANGLE     (1)                                                                              (2)      (3)                                                                              (4)                                             __________________________________________________________________________    1    .0000     .0000                                                                            .0000    .0000                                                                            .0000                                           2    3.3787    .0000                                                                            .1701    .0000                                                                            .0000                                           3    4.8214    .0000                                                                            .2847    .0000                                                                            .0000                                           4    6.2247    .0000                                                                            .4295    .0000                                                                            .0000                                           5    7.3653    .0000                                                                            .5760    .0000                                                                            .0000                                           6    9.1918    .0000                                                                            .8749    .0000                                                                            .0000                                           7    10.0000   .0000                                                                            1.0365   .0000                                                                            .0000                                           8    13.3787   .0000                                                                            1.9870   .0000                                                                            .0000                                           9    14.8214   .0000                                                                            2.5248   .0000                                                                            .0000                                           10   16.2247   .0000                                                                            3.1268   .0000                                                                            .0000                                           11   17.3653   .0000                                                                            3.6722   .0000                                                                            .0000                                           12   19.1918   .0000                                                                            4.6460   .0000                                                                            .0000                                           13   20.0000   .0000                                                                            5.1165   .0000                                                                            .0000                                           __________________________________________________________________________    Amount of Rotation for Zooming and Amount of Rotation for Focusing of         Embodiment of Japanese Patent Application No. 5-142475                        (Rotation Amount Ratio: a.sub.F /a.sub.Z = 1.0)                                        Infinity           Amount of                                                  Corresponding                                                                             Photographing                                                                        Rotation for                                      Focal Length                                                                           Position    Distance                                                                             Focusing                                          __________________________________________________________________________    36.0 mm  .0000       5.00 m 3.379                                             50.0 mm  2.1079      3.00 m 4.821                                             60.0 mm  3.5742      2.00 m 6.225                                             70.0 mm  5.0485      1.50 m 7.365                                             85.0 mm  7.2321      1.00 m 9.192                                             103.0 mm 10.0000     0.85 m 10.000                                            __________________________________________________________________________    Condition Corresponding Value (1)                                                                  1.59                                                     Condition Corresponding Value (2)                                                                  3.94                                                     Condition Corresponding Value (3)                                                                  1.00                                                     Condition Corresponding Value (4)                                                                  5.43 (wide-angle end)                                                         4.36 (telephoto end)                                     Condition Corresponding Value (5)                                                                  2.75 (wide-angle end)                                                         3.80 (telephoto end)                                     Condition Corresponding Value (6)                                                                  0.44 (wide-angle end)                                                         0.43 (telephoto end)                                     __________________________________________________________________________

Table 2 below summarizes the numerical value data of the cams of thefocusing lens unit in the embodiment of Japanese Patent ApplicationLaid-Open No. 5-142475, which data are calculated by interpolation basedon a spline function on the basis of the sample data of the focus camsummarized in the middle table in Table 1. In this table, (ANGLE) is theangle of rotation of the rotatable lens barrel, (2) is the amount (mm)of movement, in the direction of the optical axis, of the second lensunit, and (F) is the focal length (mm) of the entire system in aninfinity in-focus state corresponding to the amount (ANGLE) of rotation.

                  TABLE 2                                                         ______________________________________                                        Cam Numerical Value Data of Focusing Lens Unit in Embodiment of               Japanese Patent Application Laid-Open No. 5-142475                            Focus Cam        Zoom Compensation Cam                                        Numerical Value Data                                                                           Numerical Value Data                                         ANGLE (2)      F         ANGLE  (2)    F                                      ______________________________________                                        .0000 .0000    36.0000   .0000  .0000  36.0000                                .5000 .0208    39.1417   .5000  .0208  39.1417                                1.0000                                                                              .0423    42.4381   1.0000 .5684  42.4381                                1.5000                                                                              .0649    45.8280   1.5000 .8335  45.8280                                2.0000                                                                              .0892    49.2589   2.0000 1.0810 49.2589                                2.5000                                                                              .1158    52.6890   2.5000 1.3090 52.6890                                3.0000                                                                              .1454    56.1033   3.0000 1.5167 56.1033                                3.5000                                                                              .1785    59.4978   3.5000 1.7038 59.4978                                4.0000                                                                              .2154    62.8763   4.0000 1.8710 62.8763                                4.5000                                                                              .2563    66.2597   4.5000 2.0204 66.2597                                5.0000                                                                              .3012    69.6675   5.0000 2.1534 69.6675                                5.5000                                                                              .3503    73.1066   5.5000 2.2712 73.1066                                6.0000                                                                              .4039    76.5591   6.0000 2.3738 76.5591                                6.5000                                                                              .4623    80.0055   6.5000 2.4616 80.0055                                7.0000                                                                              .5260    83.4263   7.0000 2.5347 83.4263                                7.5000                                                                              .5953    86.8023   7.5000 2.5931 86.8023                                8.0000                                                                              .6705    90.1274   8.0000 2.6372 90.1274                                8.5000                                                                              .7518    93.4109   8.5000 2.6680 93.4109                                9.0000                                                                              .8395    96.6628   9.0000 2.6860 96.6628                                9.5000                                                                              .9340    99.8856   9.5000 2.6916 99.8856                                10.0000                                                                             1.0365   103.0000  10.0000                                                                              2.6814 103.0000                               10.5000                                                                             1.1489   .0000                                                          11.0000                                                                             1.2714   .0000                                                          11.5000                                                                             1.4038   .0000                                                          12.0000                                                                             1.5460   .0000                                                          12.5000                                                                             1.6977   .0000                                                          13.0000                                                                             1.8588   .0000                                                          13.5000                                                                             2.0292   .0000                                                          14.0000                                                                             2.2088   .0000                                                          14.5000                                                                             2.3980   .0000                                                          15.0000                                                                             2.5971   .0000                                                          15.5000                                                                             2.8062   .0000                                                          16.0000                                                                             3.0252   .0000                                                          16.5000                                                                             3.2540   .0000                                                          17.0000                                                                             3.4924   .0000                                                          17.5000                                                                             3.7397   .0000                                                          18.0000                                                                             3.9959   .0000                                                          18.5000                                                                             4.2617   .0000                                                          19.0000                                                                             4.5374   .0000                                                          19.5000                                                                             4.8236   .0000                                                          20.0000                                                                             5.1165   .0000                                                          ______________________________________                                    

The left table in Table 2 summarizes the numerical value data of thefocus cam in the embodiment of Japanese Patent Application Laid-Open No.5-142475, and the right table in Table 2 summarizes the numerical valuedata of the zoom compensation cam of the embodiment. A value obtained bysynthesizing the amount (2) of movement in the direction of the opticalaxis in the numerical value data of the focus cam and the amount (2) ofmovement in the direction of the optical axis in the numerical valuedata of the zoom compensation cam in a range from the amount of rotation(ANGLE=0.0) to the amount of rotation (ANGLE=10.0) agrees with themovement locus of the second lens unit calculated using the paraxialdata in the upper table in Table 1.

Tables 3, 4, and 5 below summarize the amount DX (mm) of movement forfocusing, in the direction of the optical axis, of the focusing lensunit, the imaging magnifications β_(K) of the respective lens units, theconversion coefficient γ_(x) associated with the direction of theoptical axis, the slope (dx/da) of the focus cam, and the conversioncoefficient γ_(a) associated with the direction of rotation at thewide-angle end (F=36.0), the middle position (F=50.0), and the telephotoend (F=103.0), respectively. In these tables, (R) on the left side isthe photographing distance (m), (ANG) is the amount of rotation on thefocus cam upon focusing to the respective photographing distances, and1), 2), 3), and 4) on the right side respectively represent the first,second, third, and fourth lens units. Also, in these tables, the firsttable summarizes the amount DX (mm) of movement for focusing in thedirection of the optical axis upon focusing to the respectivephotographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.85 m)(note that movement toward the object side is positive). The secondtable summarizes the imaging magnifications PK of the respective lensunits in an in-focus state at the respective photographing distances(R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.85 m). The third tablesummarizes the conversion coefficient γ_(x) associated with thedirection of the optical axis of the focusing lens unit in an in-focusstate at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0,1.5, 1.0, and 0.85 m). Furthermore, the fourth table summarizes theslope (dx/da) of the focus cam at the positions, on the focus cam,corresponding to an in-focus state at the respective photographingdistances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.85 m), and the fifthtable summarizes the conversion coefficient γ_(a) associated with thedirection of rotation of the focusing lens unit in an in-focus state atthe respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0,and 0.85 m).

                  TABLE 3                                                         ______________________________________                                        Amount DX (mm) of Movement for Focusing in Direction of                       Optical Axis at Wide-angle End (36.0 mm) in                                   Japanese Patent Application Laid-Open No. 5-142475                            R   .000 ANG  .000 1)  .000 2)                                                                              .000 3)                                                                              .000 4)                                                                              .000                              R   10.000 ANG                                                                              1.912 1) .000 2)                                                                              .085 3)                                                                              .000 4)                                                                              .000                              R   5.000 ANG 3.379 1) .000 2)                                                                              .170 3)                                                                              .000 4)                                                                              .000                              R   3.000 ANG 4.821 1) .000 2)                                                                              .285 3)                                                                              .000 4)                                                                              .000                              R   2.000 ANG 6.225 1) .000 2)                                                                              .429 3)                                                                              .000 4)                                                                              .000                              R   1.500 ANG 7.365 1) .000 2)                                                                              .576 3)                                                                              .000 4)                                                                              .000                              R   1.000 ANG 9.192 1) .000 2)                                                                              .875 3)                                                                              .000 4)                                                                              .000                              R   .850 ANG  10.000 1)                                                                              .000 2)                                                                              1.037 3)                                                                             .000 4)                                                                              .000                              Imaging Magnification β.sub.K of Lens Units at Wide-angle End (36.0      mm)                                                                           in Japanese Patent Application Laid-Open No. 5-142475                         R   .000 ANG  .000 1)  .000 2)                                                                              -.377 3)                                                                             -9.721 4)                                                                            .138                              R   10.000 ANG                                                                              1.912 1) -.007 2)                                                                             -.372 3)                                                                             -9.721 4)                                                                            .138                              R   5.000 ANG 3.379 1) -.015 2)                                                                             -.367 3)                                                                             -9.721 4)                                                                            .138                              R   3.000 ANG 4.821 1) -.025 2)                                                                             -.360 3)                                                                             -9.721 4)                                                                            .138                              R   2.000 ANG 6.225 1) -.039 2)                                                                             -.352 3)                                                                             -9.721 4)                                                                            .138                              R   1.500 ANG 7.365 1) -.054 2)                                                                             -.343 3)                                                                             -9.721 4)                                                                            .138                              R   1.000 ANG 9.192 1) -.088 2)                                                                             -.325 3)                                                                             -9.721 4)                                                                            .138                              R   .850 ANG  10.000 1)                                                                              -.107 2)                                                                             -.316 3)                                                                             -9.721 4)                                                                            .138                              Conversion Coefficient γ.sub.x Associated With Direction of             Optical Axis at Wide-angle End (36.0 mm) in                                   Japanese Patent Application Laid-Open No. 5-142475                            R   .000 ANG  .000 1)  .000 2)                                                                              1.533 3)                                                                             .000 4)                                                                              .000                              R   10.000 ANG                                                                              1.912 1) .000 2)                                                                              1.540 3)                                                                             .000 4)                                                                              .000                              R   5.000 ANG 3.379 1) .000 2)                                                                              l.547 3)                                                                             .000 4)                                                                              .000                              R   3.000 ANG 4.821 1) .000 2)                                                                              1.556 3)                                                                             .000 4)                                                                              .000                              R   2.000 ANG 6.225 1) .000 2)                                                                              1.567 3)                                                                             .000 4)                                                                              .000                              R   1.500 ANG 7.365 1) .000 2)                                                                              1.578 3)                                                                             .000 4)                                                                              .000                              R   1.000 ANG 9.192 1) .000 2)                                                                              1.599 3)                                                                             .000 4)                                                                              .000                              R   .850 ANG  10.000 1)                                                                              .000 2)                                                                              1.610 3)                                                                             .000 4)                                                                              .000                              Slope dx/da of Focus Cam at Wide-angle End (36.0 mm) in                       Japanese Patent Application Laid-Open No. 5-142475                            R   .000 ANG  .000 1)  .000 2)                                                                              .041 3)                                                                              .000 4)                                                                              .000                              R   10.000 ANG                                                                              1.912 1) .000 2)                                                                              .050 3)                                                                              .000 4)                                                                              .000                              R   5.000 ANG 3.379 1) .000 2)                                                                              .068 3)                                                                              .000 4)                                                                              .000                              R   3.000 ANG 4.821 1) .000 2)                                                                              .091 3)                                                                              .000 4)                                                                              .000                              R   2.000 ANG 6.225 1) .000 2)                                                                              .116 3)                                                                              .000 4)                                                                              .000                              R   1.500 ANG 7.365 1) .000 2)                                                                              .141 3)                                                                              .000 4)                                                                              .000                              R   1.000 ANG 9.192 1) .000 2)                                                                              .187 3)                                                                              .000 4)                                                                              .000                              R   .850 ANG  10.000 1)                                                                              .000 2)                                                                              .215 3)                                                                              .000 4)                                                                              .000                              Conversion Coefficient γ.sub.a Associated With Direction of             Rotation at Wide-angle End (36.0 mm) in                                       Japanese Patent Application Laid-Open No. 5-142475                            R   .000 ANG  .000 1)  .000 2)                                                                              .064 3)                                                                              .000 4)                                                                              .000                              R   10.000 ANG                                                                              1.912 1) .000 2)                                                                              .077 3)                                                                              .000 4)                                                                              .000                              R   5.000 ANG 3.379 1) .000 2)                                                                              .105 3)                                                                              .000 4)                                                                              .000                              R   3.000 ANG 4.821 1) .000 2)                                                                              .141 3)                                                                              .000 4)                                                                              .000                              R   2.000 ANG 6.225 1) .000 2)                                                                              .182 3)                                                                              .000 4)                                                                              .000                              R   1.500 ANG 7.365 1) .000 2)                                                                              .223 3)                                                                              .000 4)                                                                              .000                              R   1.000 ANG 9.192 1) .000 2)                                                                              .299 3)                                                                              .000 4)                                                                              .000                              R   .850 ANG  10.000 1)                                                                              .000 2)                                                                              .346 3)                                                                              .000 4)                                                                              .000                              ______________________________________                                         Condition Corresponding Values: γ.sub.xR /γ.sub.xO = 1.05,        γ.sub.aR /γ.sub.aO = 5.43                                    

                                      TABLE 4                                     __________________________________________________________________________    Amount DX (mm) of Movement for Focusing in Direction of Optical Axis at       Middle Position (50.0 mm) in Japanese Patent Application Laid-Open No.        5-142475                                                                      R  .000 ANG                                                                             .000 1)                                                                             .000 2)                                                                             .000 3)                                                                             .000 4)                                                                              .000                                       R  10.000 ANG                                                                           1.972 1)                                                                            .000 2)                                                                             .127 3)                                                                             .000 4)                                                                              .000                                       R  5.000 ANG                                                                            3.373 1)                                                                            .000 2)                                                                             .254 3)                                                                             .000 4)                                                                              .000                                       R  3.000 ANG                                                                            4.821 1)                                                                            .000 2)                                                                             .422 3)                                                                             .000 4)                                                                              .000                                       R  2.000 ANG                                                                            6.241 1)                                                                            .000 2)                                                                             .632 3)                                                                             .000 4)                                                                              .000                                       R  1.500 ANG                                                                            7.403 1)                                                                            .000 2)                                                                             .841 3)                                                                             .000 4)                                                                              .000                                       R  1.000 ANG                                                                            9.213 1)                                                                            .000 2)                                                                             1.261 3)                                                                            .000 4)                                                                              .000                                       R  .850 ANG                                                                             10.000 1)                                                                           .000 2)                                                                             1.483 3)                                                                            .000 4)                                                                              .000                                       Imaging Magnification β.sub.K of Lens Units at Middle Position (50.0     mm) in                                                                        Japanese Patent Application Laid-Open No. 5-142475                            R  .000 ANG                                                                             .000 1)                                                                             .000 2)                                                                             -.447 3)                                                                            -42.292 4)                                                                           .037                                       R  10.000 ANG                                                                           1.972 1)                                                                            -.007 2)                                                                            -.440 3)                                                                            -42.292 4)                                                                           .037                                       R  5.000 ANG                                                                            3.373 1)                                                                            -.015 2)                                                                            -.432 3)                                                                            -42.292 4)                                                                           .037                                       R  3.000 ANG                                                                            4.821 1)                                                                            -.025 2)                                                                            -.422 3)                                                                            -42.292 4)                                                                           .037                                       R  2.000 ANG                                                                            6.241 1)                                                                            -.040 2)                                                                            -.409 3)                                                                            -42.292 4)                                                                           .037                                       R  1.500 ANG                                                                            7.403 1)                                                                            -.055 2)                                                                            -.397 3)                                                                            -42.292 4)                                                                           .037                                       R  1.000 ANG                                                                            9.213 1)                                                                            -.089 2)                                                                            -.372 3)                                                                            -42.292 4)                                                                           .037                                       R  .850 ANG                                                                             10.000 1)                                                                           -.109 2)                                                                            -.359 3)                                                                            -42.292 4)                                                                           .037                                       Conversion Coefficient γ.sub.x Associated With Direction of Optical     Axis at Middle Position                                                       (50.0 mm) in Japanese Patent Application Laid-Open No. 5-142475               R  .000 ANG                                                                             .000 1)                                                                             .000 2)                                                                             1.966 3)                                                                            .000 4)                                                                              .000                                       R  10.000 ANG                                                                           1.972 1)                                                                            .000 2)                                                                             1.982 3)                                                                            .000 4)                                                                              .000                                       R  5.000 ANG                                                                            3.373 1)                                                                            .000 2)                                                                             1.998 3)                                                                            .000 4)                                                                              .000                                       R  3.000 ANG                                                                            4.821 1)                                                                            .000 2)                                                                             2.019 3)                                                                            .000 4)                                                                              .000                                       R  2.000 ANG                                                                            6.241 1)                                                                            .000 2)                                                                             2.045 3)                                                                            .000 4)                                                                              .000                                       R  1.500 ANG                                                                            7.403 1)                                                                            .000 2)                                                                             2.069 3)                                                                            .000 4)                                                                              .000                                       R  1.000 ANG                                                                            9.213 1)                                                                            .000 2)                                                                             2.117 3)                                                                            .000 4)                                                                              .000                                       R  .850 ANG                                                                             10.000 1)                                                                           .000 2)                                                                             2.140 3)                                                                            .000 4)                                                                              .000                                       Slope dx/da of Focus Cam at Middle Position (50.0 mm) in Japanese Patent      Application                                                                   Laid-Open No. 5-142475                                                        R  .000 ANG                                                                             .000 1)                                                                             .000 2)                                                                             .052 3)                                                                             .000 4)                                                                              .000                                       R  10.000 ANG                                                                           1.972 1)                                                                            .000 2)                                                                             .079 3)                                                                             .000 4)                                                                              .000                                       R  5.000 ANG                                                                            3.373 1)                                                                            .000 2)                                                                             .102 3)                                                                             .000 4)                                                                              .000                                       R  3.000 ANG                                                                            4.821 1)                                                                            .000 2)                                                                             .131 3)                                                                             .000 4)                                                                              .000                                       R  2.000 ANG                                                                            6.241 1)                                                                            .000 2)                                                                             .165 3)                                                                             .000 4)                                                                              .000                                       R  1.500 ANG                                                                            7.403 1)                                                                            .000 2)                                                                             .197 3)                                                                             .000 4)                                                                              .000                                       R  1.000 ANG                                                                            9.213 1)                                                                            .000 2)                                                                             .268 3)                                                                             .000 4)                                                                              .000                                       R  .850 ANG                                                                             10.000 1)                                                                           .000 2)                                                                             .298 3)                                                                             .000 4)                                                                              .000                                       Conversion Coefficient γ.sub.a Associated With Direction of             Rotation at Middle Position                                                   (50.0 mm) in Japanese Patent Application Laid-Open No. 5-142475               R  .000 ANG                                                                             .000 1)                                                                             .000 2)                                                                             .102 3)                                                                             .000 4)                                                                              .000                                       R  10.000 ANG                                                                           1.972 1)                                                                            .000 2)                                                                             .157 3)                                                                             .000 4)                                                                              .000                                       R  5.000 ANG                                                                            3.373 1)                                                                            .000 2)                                                                             .204 3)                                                                             .000 4)                                                                              .000                                       R  3.000 ANG                                                                            4.821 1)                                                                            .000 2)                                                                             .265 3)                                                                             .000 4)                                                                              .000                                       R  2.000 ANG                                                                            6.241 1)                                                                            .000 2)                                                                             .338 3)                                                                             .000 4)                                                                              .000                                       R  1.500 ANG                                                                            7.403 1)                                                                            .000 2)                                                                             .407 3)                                                                             .000 4)                                                                              .000                                       R  1.000 ANG                                                                            9.213 1)                                                                            .000 2)                                                                             .566 3)                                                                             .000 4)                                                                              .000                                       R  .850 ANG                                                                             10.000 1)                                                                           .000 2)                                                                             .638 3)                                                                             .000 4)                                                                              .000                                       __________________________________________________________________________     Condition Corresponding Values: γ.sub.xR /γ.sub.xO = 1.09,        γ.sub.aR /γ.sub.aO = 6.26                                    

                  TABLE 5                                                         ______________________________________                                        Amount DX (mm) of Movement for Focusing in Direction of                       Optical Axis at Telephoto End (103.0 mm) in                                   Japanese Patent Application Laid-Open No. 5-142475                            R   .000 ANG  .000 1)  .000 2)                                                                              .000 3)                                                                              .000 4)                                                                              .000                              R   10.000 ANG                                                                              1.975 1) .000 2)                                                                              .502 3)                                                                              .000 4)                                                                              .000                              R   5.000 ANG 3.379 1) .000 2)                                                                              .951 3)                                                                              .000 4)                                                                              .000                              R   3.000 ANG 4.821 1) .000 2)                                                                              1.488 3)                                                                             .000 4)                                                                              .000                              R   2.000 ANG 6.225 1) .000 2)                                                                              2.090 3)                                                                             .000 4)                                                                              .000                              R   1.500 ANG 7.365 1) .000 2)                                                                              2.636 3)                                                                             .000 4)                                                                              .000                              R   1.000 ANG 9.192 1) .000 2)                                                                              3.609 3)                                                                             .000 4)                                                                              .000                              R   .850 ANG  10.000 1)                                                                              .000 2)                                                                              4.080 3)                                                                             .000 4)                                                                              .000                              Imaging Magnification β.sub.K of Lens Units at Telephoto End (103.0      mm)                                                                           in Japanese Patent Application Laid-Open No. 5-142475                         R   .000 ANG  .000 1)  .000 2)                                                                              -.716 3)                                                                             13.060 4)                                                                            -.154                             R   10.000 ANG                                                                              1.975 1) -.007 2)                                                                             -.686 3)                                                                             13.060 4)                                                                            -.154                             R   5.000 ANG 3.379 1) -.015 2)                                                                             -.659 3)                                                                             13.060 4)                                                                            -.154                             R   3.000 ANG 4.821 1) -.026 2)                                                                             -.627 3)                                                                             13.060 4)                                                                            -.154                             R   2.000 ANG 6.225 1) -.040 2)                                                                             -.592 3)                                                                             13.060 4)                                                                            -.154                             R   1.500 ANG 7.365 1) -.055 2)                                                                             -.559 3)                                                                             13.060 4)                                                                            -.154                             R   1.000 ANG 9.192 1) -.090 2)                                                                             -.501 3)                                                                             13.060 4)                                                                            -.154                             R   .850 ANG  10.000 1)                                                                              -.112 2)                                                                             -.473 3)                                                                             13.060 4)                                                                            -.154                             Conversion Coefficient γ.sub.x Associated With Direction of             Optical Axis at Telephoto End (103.0 mm) in                                   Japanese Patent Application Laid-Open No. 5-142475                            R   .000 ANG  .000 1)  .000 2)                                                                              1.982 3)                                                                             .000 4)                                                                              .000                              R   10.000 ANG                                                                              1.975 1) .000 2)                                                                              2.152 3)                                                                             .000 4)                                                                              .000                              R   5.000 ANG 3.379 1) .000 2)                                                                              2.298 3)                                                                             .000 4)                                                                              .000                              R   3.000 ANG 4.821 1) .000 2)                                                                              2.465 3)                                                                             .000 4)                                                                              .000                              R   2.000 ANG 6.225 1) .000 2)                                                                              2.643 3)                                                                             .000 4)                                                                              .000                              R   1.500 ANG 7.365 1) .000 2)                                                                              2.795 3)                                                                             .000 4)                                                                              .000                              R   1.000 ANG 9.192 1) .000 2)                                                                              3.044 3)                                                                             .000 4)                                                                              .000                              R   .850 ANG  10.000 1)                                                                              .000 2)                                                                              3.155 3)                                                                             .000 4)                                                                              .000                              Slope dx/da of Focus Cam at Telephoto End (103.0 mm) in                       Japanese Patent Application Laid-Open No. 5-142475                            R   .000 ANG  .000 1)  .000 2)                                                                              .215 3)                                                                              .000 4)                                                                              .000                              R   10.000 ANG                                                                              1.975 1) .000 2)                                                                              .293 3)                                                                              .000 4)                                                                              .000                              R   5.000 ANG 3.379 1) .000 2)                                                                              .345 3)                                                                              .000 4)                                                                              .000                              R   3.000 ANG 4.821 1) .000 2)                                                                              .401 3)                                                                              .000 4)                                                                              .000                              R   2.000 ANG 6.225 1) .000 2)                                                                              .457 3)                                                                              .000 4)                                                                              .000                              R   1.500 ANG 7.365 1) .000 2)                                                                              .499 3)                                                                              .000 4)                                                                              .000                              R   1.000 ANG 9.192 1) .000 2)                                                                              .570 3)                                                                              .000 4)                                                                              .000                              R   .850 ANG  10.000 1)                                                                              .000 2)                                                                              .588 3)                                                                              .000 4)                                                                              .000                              Conversion Coefficient γ.sub.a Associated With Direction of             Rotation at Telephoto End (103.0 mm) in                                       Japanese Patent Application Laid-Open No. 5-142475                            R   .000 ANG  .000 1)  .000 2)                                                                              .425 3)                                                                              .000 4)                                                                              .000                              R   10.000 ANG                                                                              1.975 1) .000 2)                                                                              .630 3)                                                                              .000 4)                                                                              .000                              R   5.000 ANG 3.379 1) .000 2)                                                                              .794 3)                                                                              .000 4)                                                                              .000                              R   3.000 ANG 4.821 1) .000 2)                                                                              .989 3)                                                                              .000 4)                                                                              .000                              R   2.000 ANG 6.225 1) .000 2)                                                                              1.207 3)                                                                             .000 4)                                                                              .000                              R   1.500 ANG 7.365 1) .000 2)                                                                              1.394 3)                                                                             .000 4)                                                                              .000                              R   1.000 ANG 9.192 1) .000 2)                                                                              1.736 3)                                                                             .000 4)                                                                              .000                              R   .850 ANG  10.000 1)                                                                              .000 2)                                                                              1.855 3)                                                                             .000 4)                                                                              .000                              ______________________________________                                         Condition Corresponding Values: γ.sub.xR /γ.sub.xO = 1.59,        γ.sub.aR /γ.sub.aO = 4.36                                    

As can be seen from Tables 3, 4, and 5, the conversion coefficient γ_(X)associated with the direction of the optical axis and the slope (dx/da)of the focus cam at the respective focal lengths increase as thephotographing distance becomes closer to the closest distance.Therefore, as can be seen from these tables, the conversion coefficientγ_(a) associated with the direction of rotation, which is defined as theproduct of γ_(x) and (dx/da), further increases.

More specifically, in a zoom lens in which the conversion coefficientγ_(X) associated with the amount x of movement, in the direction of theoptical axis, of the focusing lens unit in a closest in-focus state islarger than that in an infinity in-focus state, i.e., which satisfies:

    1.0<γ.sub.xR /γ.sub.xO

when the focus cam which satisfies the following inequality, i.e., thefocus cam has a shape having a larger slope (dx/da) at the closestcorresponding position than that at the infinity corresponding position:

    1.0<(dx/da).sub.R /(dx/da).sub.O

the following inequality is satisfied:

    1.0<γ.sub.xR /γ.sub.xO <γ.sub.aR /γ.sub.aO

The rate of change, from the infinity in-focus value (γ_(aO)) to theclosest in-focus value (γ_(aR)), of the conversion coefficient γ_(a)associated with the angle a of rotation of the rotatable lens barrelundesirably becomes larger than the rate of change, from the infinityin-focus value (γ_(xO)) to the closest in-focus value (γ_(xR)), of theconversion coefficient γ_(x) associated with the amount x of movement inthe direction of the optical axis.

From Tables 3, 4, and 5 above, the rate of change of γ_(a) is ×5.43 atthe wide-angle end (F=36.0), ×6.26 at the middle position (F=50.0), and×4.36 at the telephoto-end (F=103.0).

As described above, when the conversion coefficient γ changes incorrespondence with the lens arrangement (e.g., focusing), as describedin Japanese Patent Application Laid-Open No. 3-228006, a plurality ofpairs of data of the conversion coefficient γ and the correctioncoefficient γ must be stored in the storage means in units of aplurality of divided focus ranges. Therefore, when the rate of change ofγ_(a) is large (γ_(aR) /γ_(aO) >>1.0), the number of divisionsincreases, and the storage capacity inevitably becomes large, resultingin an increase in cost. For example, when a change in γ_(a) in a singlefocus range is divided under the condition defined by the followinginequality:

    γ.sub.max /γ.sub.min <1.2

the number N of divisions is expressed by inequality (a) below:

    N>log(γ.sub.MAX /γ.sub.MIN)/log (1.2)          (a)

Therefore, the numbers N_(W), N_(M), and N_(T) of divisions at thewide-angle end, middle position, and telephoto end have large values asfollows:

    N.sub.W >9.3 N.sub.M >10.1 N.sub.T >8.1

The formula K=γ(1+γ.ΔBf) presented by Japanese Patent ApplicationLaid-Open No. 62-170924 is rewritten to the conversion coefficient K_(a)associated with the angle a of rotation of the rotatable lens barrel:

    K.sub.a =γ.sub.a (1+γ.ΔBf)

Then, the following formula is defined by using a correction coefficientμ (γ=-1/μ):

    K.sub.a =γ.sub.a (1-ΔBf/μ)

Tables 6, 7, and 8 below summarize the calculation results of the valuesof the conversion coefficient K_(a) and the correction coefficient μaccording to the embodiment of Japanese Patent Application Laid-Open No.5-142475 at the wide-angle end (F=36.0), middle position (F=50.0), andtelephoto end (F=103.0) using the above formula.

In these tables, (R) is the object distance (m), (ANG) is the amount ofrotation for focusing from the infinity corresponding position on thefocus cam, (r) is the conversion coefficient γ_(a) in the direction ofrotation, (rs) is the conversion coefficient K_(a), (bf) is the defocusamount (mm), and (l) is the correction coefficient μ. Each table has amatrix structure, and eight rows in the vertical direction indicated by(POS) represent the object positions (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0,and 0.85 mm), and four pairs (R, ANGLE) in the horizontal directionrepresent the lens arrangements of the focusing lens unit.

More specifically, the position of the focusing lens in the first pairin the upper two tables in each of Tables 6, 7, and 8, i.e., in thethird and fourth columns is (R, ANGLE)=(0.0, 0.0), and it indicates thatthis position corresponds to the infinity corresponding position.Therefore, the third column (r) in the first table represents the valueof the conversion coefficient γ_(a) in the direction of rotation whenthe focusing lens unit is focused on an infinity object, and the fourthcolumn (rs) represents the value of the conversion coefficient K_(a)when the focusing lens unit is moved from an in-focus state on aninfinity object to an in-focus state at the object distance in thesecond column. Furthermore, the third column (bf) in the second tablerepresents the defocus amount ABf from a predetermined imaging positionwhen the position of the focusing lens unit corresponds to the infinitycorresponding position, and the object is located at an object distancein the second column, and the fourth column (l) represents the value ofthe correction coefficient μ when the focusing lens unit is moved froman in-focus state on an infinity object to an in-focus state at theobject distance in the second column.

Similarly, the position of the focusing lens in the fourth pair in thelower two tables in each of Tables 6, 7, and 8, i.e., in the ninth and10th columns is (R, ANGLE)=(0.85, 10.0), and it indicates that thisposition corresponds to the closest in-focus (R=0.85 m) correspondingposition. Therefore, the ninth column (r) in the third table representsthe value of the conversion coefficient γ_(a) in the direction ofrotation when the focusing lens unit is focused on a closest distance(R=0.85 m) object, and the 10th column (rs) represents the value of theconversion coefficient K_(a) when the focusing lens unit is moved froman in-focus state on the closest distance (R=0.85 m) object to anin-focus state at the object distance in the second column. Furthermore,the ninth column (bf) in the fourth table represents the defocus amountΔBf from a predetermined imaging position when the position of thefocusing lens unit corresponds to the closest corresponding position,and the object is located at an object distance in the second column,and the 10th column (l) represents the value of the correctioncoefficient μ when the focusing lens unit is moved from an in-focusstate on the closest distance (R=0.85 m) object to an in-focus state atthe object distance in the second column.

From the above formulas, since the conversion coefficient in thedirection of rotation is calculated by K_(a) =ΔBf/Δa (where Δa: theamount of rotation for focusing), and the correction coefficient μ iscalculated by μ=ΔBf/(1-K_(a) /γ_(a)), the value of the conversioncoefficient K_(a) (eighth row, fourth column in first table: 0.175) whenthe focusing lens unit is moved from an in-focus state on the infinityobject to an in-focus state at the object distance (R=0.85 m) in Table 6is calculated by K_(a) =1.75/10.0=0.175 using ΔBf=1.75 and Δa=10.0. Onthe other hand, the value of the correction coefficient μ (eighth row,fourth column in second table: -1.00) is calculated as μ=-1.00 usingΔBf=1.75, K_(a) =0.175, and γ_(a) =0.064.

                                      TABLE 6                                     __________________________________________________________________________    Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associated        with Direction of Rotation and Correction                                     Coefficient μ: (l) at Wide-angle End (36.0 mm) of Embodiment of            Japanese Patent Application Laid-Open No. 5-142475                            f = 36.0 mm                                                                   __________________________________________________________________________    (R,ANGLE) =                                                                            .000 .000 10.000                                                                             1.912                                                                              5.000                                                                              3.379                                                                              3.000                                                                              4.821                             __________________________________________________________________________    POS R    r    rs   r    rs   r    rs   r    rs                                __________________________________________________________________________    1   .000 .064 .000      .068      .077      .090                              2   10.000    .069 .077 .000      .089      .105                              3   5.000     .078      .090 .105 .000      .122                              4   3.000     .093      .108      .124 .142 .000                              5   2.000     .110      .127      .144      .163                              6   1.500     .126      .145      .163      .183                              7   1.000     .158      .180      .200      .221                              8   .850      .175      .197      .219      .241                              __________________________________________________________________________    POS R    bf   l    bf   l    bf   l    bf   l                                 __________________________________________________________________________    1   .000 .00  .00  -.13 -1.08                                                                              -.26 -.95 -.43 -1.18                             2   10.000                                                                             .13  -1.71                                                                              .00  .00  -.13 -.86 -.31 -1.19                             3   5.000                                                                              .26  -1.14                                                                              .13  -.77 .00  .00  -.18 -1.30                             4   3.000                                                                              .45  -.97 .31  -.78 .18  -1.00                                                                              .00  .00                               5   2.000                                                                              .68  -.94 .55  -.84 .41  -1.11                                                                              .23  -1.53                             6   1.500                                                                              .93  -.94 .79  -.90 .65  -1.18                                                                              .47  -1.59                             7   1.000                                                                              1.45 -.98 1.31 -.98 1.16 -1.29                                                                              .97  -1.71                             8   .850 1.75 -1.00                                                                              1.60 -1.02                                                                              1.45 -1.34                                                                              1.25 -1.77                             __________________________________________________________________________    (R,ANGLE) =                                                                            2.000                                                                              6.225                                                                              1.500                                                                              7.365                                                                              1.000                                                                              9.192                                                                              .850 10.000                            __________________________________________________________________________    POS R    r    rs   r    rs   r    rs   r    rs                                __________________________________________________________________________    1   .000      .104      .117      .141      .153                              2   10.000    .121      .136      .162      .175                              3   5.000     .140      .155      .182      .196                              4   3.000     .160      .176      .205      .219                              5   2.000                                                                              .182 .000      .200      .231      .246                              6   1.500     .204 .223 .000      .255      .271                              7   1.000     .245      .265 .299 .000      .318                              8   .850      .266      .287      .324 .346 .000                              __________________________________________________________________________    POS R    bf   l    bf   l    bf   l    bf   l                                 __________________________________________________________________________    1   .000 -.65 -1.51                                                                              -.86 -1.82                                                                              -1.30                                                                              -2.46                                                                              -1.53                                                                              -2.74                             2   10.000                                                                             -.52 -1.57                                                                              -.74 -1.91                                                                              -1.18                                                                              -2.58                                                                              -1.41                                                                              -2.86                             3   5.000                                                                              -.40 -1.69                                                                              -.62 -2.03                                                                              -1.06                                                                              -2.72                                                                              -1.30                                                                              -2.99                             4   3.000                                                                              -.22 -1.79                                                                              -.45 -2.14                                                                              -.90 -2.85                                                                              -1.14                                                                              -3.11                             5   2.000                                                                              .00  .00  -.23 -2.24                                                                              -.69 -3.00                                                                              -.93 -3.22                             6   1.500                                                                              .23  -1.97                                                                              .00  .00  -.47 -3.15                                                                              -.71 -3.29                             7   1.000                                                                              .73  -2.13                                                                              .48  -2.55                                                                              .00  .00  -.26 -3.16                             8   .850 1.00 -2.19                                                                              .76  -2.62                                                                              .26  -3.15                                                                              .00  .00                               __________________________________________________________________________     Condition Corresponding Values: K.sub.aO /γ.sub.aO = 2.75, K.sub.aR     /γ.sub.aR = 0.44                                                   

                                      TABLE 7                                     __________________________________________________________________________    Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associated        with Direction of Rotation and Correction                                     Coefficient μ: (l) at Middle Position (50.0 mm) of Embodiment of           Japanese Patent Application Laid-Open No. 5-142475                            f = 50.0 mm                                                                   __________________________________________________________________________    (R,ANGLE) =                                                                            .000 .000 10.000                                                                             1.972                                                                              5.000                                                                              3.373                                                                              3.000                                                                              4.821                             __________________________________________________________________________    POS R    r    rs   r    rs   r    rs   r    rs                                __________________________________________________________________________    1   .000 .102 .000      .126      .146      .169                              2   10.000    .128 .157 .000      .178      .203                              3   5.000     .152      .182 .204 .000      .231                              4   3.000     .180      .212      .236 .265 .000                              5   2.000     .213      .247      .274      .305                              6   1.500     .244      .281      .310      .343                              7   1.000     .308      .350      .383      .421                              8   .850      .342      .387      .422      .462                              __________________________________________________________________________    POS R    bf   l    bf   l    bf   l    bf   l                                 __________________________________________________________________________    1   .000 .00  .00  -.25 -1.26                                                                              -.49 -1.74                                                                              -.82 -2.25                             2   10.000                                                                             .25  -.98 .00  .00  -.25 -1.97                                                                              -.58 -2.45                             3   5.000                                                                              .51  -1.04                                                                              .25  -1.61                                                                              .00  .00  -.33 -2.57                             4   3.000                                                                              .87  -1.13                                                                              .60  -1.72                                                                              .34  -2.17                                                                              .00  .00                               5   2.000                                                                              1.33 -1.22                                                                              1.06 -1.83                                                                              .79  -2.29                                                                              .43  -2.87                             6   1.500                                                                              1.81 -1.29                                                                              1.53 -1.92                                                                              1.25 -2.41                                                                              .88  -3.02                             7   1.000                                                                              2.84 -1.40                                                                              2.53 -2.06                                                                              2.24 -2.55                                                                              1.85 -3.15                             8   .850 3.42 -1.45                                                                              3.11 -2.12                                                                              2.80 -2.62                                                                              2.39 -3.22                             __________________________________________________________________________    (R,ANGLE) =                                                                            2.000                                                                              6.241                                                                              1.500                                                                              7.403                                                                              1.000                                                                              9.213                                                                              .850 10.000                            __________________________________________________________________________    POS R    r    rs   r    rs   r    rs   r    rs                                __________________________________________________________________________    1   .000      .194      .216      .256      .275                              2   10.000    .230      .253      .296      .317                              3   5.000     .259      .284      .330      .352                              4   3.000     .296      .322      .372      .396                              5   2.000                                                                              .338 .000      .365      .421      .446                              6   1.500     .377 .407 .000      .470      .497                              7   1.000     .461      .500 .566 .000      .593                              8   .850      .505      .546      .612 .638 .000                              __________________________________________________________________________    POS R    bf   l    bf   l    bf   l    bf   l                                 __________________________________________________________________________    1   .000 -1.21                                                                              -2.85                                                                              -1.60                                                                              -3.41                                                                              -2.36                                                                              -4.30                                                                              -2.75                                                                              -4.83                             2   10.000                                                                             -.98 -3.06                                                                              -1.38                                                                              -3.64                                                                              -2.15                                                                              -4.50                                                                              -2.54                                                                              -5.06                             3   5.000                                                                              -.74 -3.21                                                                              -1.15                                                                              -3.80                                                                              -1.93                                                                              -4.63                                                                              -2.34                                                                              -5.22                             4   3.000                                                                              -.42 -3.39                                                                              -.83 -3.99                                                                              -1.63                                                                              -4.76                                                                              -2.05                                                                              -5.39                             5   2.000                                                                              .00  .00  -.42 -4.15                                                                              -1.25                                                                              -4.87                                                                              -1.68                                                                              -5.58                             6   1.500                                                                              .44  -3.78                                                                              .00  .00  -.85 -5.02                                                                              -1.29                                                                              -5.84                             7   1.000                                                                              1.37 -3.74                                                                              .91  -3.96                                                                              .00  .00  -.47 -6.54                             8   .850 1.90 -3.82                                                                              1.42 -4.16                                                                              .48  -5.98                                                                              .00  .00                               __________________________________________________________________________     Condition Corresponding Values: K.sub.aO /γ.sub.aO = 3.36, K.sub.aR     /γ.sub.aR = 0.43                                                   

                                      TABLE 8                                     __________________________________________________________________________    Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associated        with Direction of Rotation and Correction                                     Coefficient μ: (l) at Telephoto End (103.0 mm) of Embodiment of            Japanese Patent Application Laid-Open No. 5-142475                            f = 103.0 mm                                                                  __________________________________________________________________________    (R,ANGLE) =                                                                            .000 .000 10.000                                                                             1.975                                                                              5.000                                                                              3.379                                                                              3.000                                                                              4.821                             __________________________________________________________________________    POS R    r    rs   r    rs   r    rs   r    rs                                __________________________________________________________________________    1   .000 .425 .000      .505      .560      .614                              2   10.000    .548 .631 .000      .686      .741                              3   5.000     .653      .738 .794 .000      .850                              4   3.000     .784      .872      .930 .989 .000                              5   2.000     .944      1.036     1.096     1.155                             6   1.500     1.103     1.198     1.258     1.316                             7   1.000     1.432     1.530     1.588     1.640                             8   .850      1.618     1.715     1.771     1.818                             __________________________________________________________________________    POS R    bf   l    bf   l    bf   l    bf   l                                 __________________________________________________________________________    1   .000 .00  .00  -1.00                                                                              -5.02                                                                              -1.89                                                                              -6.41                                                                              -2.96                                                                              -7.81                             2   10.000                                                                             1.08 -3.76                                                                              .00  .00  -.96 -7.06                                                                              -2.11                                                                              -8.40                             3   5.000                                                                              2.21 -4.12                                                                              1.04 -6.07                                                                              .00  .00  -1.23                                                                              -8.76                             4   3.000                                                                              3.78 -4.48                                                                              2.48 -6.48                                                                              1.34 -7.84                                                                              .00  .00                               5   2.000                                                                              5.88 -4.82                                                                              4.40 -6.85                                                                              3.12 -8.21                                                                              1.62 -9.63                             6   1.500                                                                              8.12 -5.10                                                                              6.46 -7.18                                                                              5.02 -8.58                                                                              3.35 -10.10                            7   1.000                                                                              13.17                                                                              -5.56                                                                              11.04                                                                              -7.74                                                                              9.23 -9.23                                                                              7.17 -10.88                            8   .850 16.18                                                                              -5.77                                                                              13.77                                                                              -8.00                                                                              11.73                                                                              -9.53                                                                              9.41 -11.22                            __________________________________________________________________________    (R,ANGLE) =                                                                            2.000                                                                              6.225                                                                              1.500                                                                              7.365                                                                              1.000                                                                              9.192                                                                              .850 10.000                            __________________________________________________________________________    POS R    r    rs   r    rs   r    rs   r    rs                                __________________________________________________________________________    1   .000      .666      .707      .769      .794                              2   10.000    .794      .835      .895      .919                              3   5.000     .904      .945      1.003     1.026                             4   3.000     1.043     1.082     1.136     1.157                             5   2.000                                                                              1.207                                                                              .000      1.242     1.290     1.307                             6   1.500     1.364                                                                              1.394                                                                              .000      1.436     1.451                             7   1.000     1.678     1.701                                                                              1.736                                                                              .000      1.733                             8   .850      1.850     1.867     1.882                                                                              1.856                                                                              .000                              __________________________________________________________________________    POS R    bf   l    bf   l    bf   l    bf   l                                 __________________________________________________________________________    1   .000 -4.15                                                                              -9.25                                                                              -5.21                                                                              -10.58                                                                             -7.07                                                                              -12.68                                                                             -7.94                                                                              -13.89                            2   10.000                                                                             -3.37                                                                              -9.85                                                                              -4.50                                                                              -11.22                                                                             -6.46                                                                              -13.33                                                                             -7.38                                                                              -14.62                            3   5.000                                                                              -2.57                                                                              -10.27                                                                             -3.77                                                                              -11.71                                                                             -5.83                                                                              -13.81                                                                             -6.80                                                                              -15.21                            4   3.000                                                                              -1.46                                                                              -10.78                                                                             -2.75                                                                              -12.32                                                                             -4.96                                                                              -14.36                                                                             -5.99                                                                              -15.91                            5   2.000                                                                              .00  .00  -1.42                                                                              -13.04                                                                             -3.83                                                                              -14.87                                                                             -4.94                                                                              -16.71                            6   1.500                                                                              1.56 -11.96                                                                             .00  .00  -2.62                                                                              -15.19                                                                             -3.82                                                                              -17.53                            7   1.000                                                                              4.98 -12.75                                                                             3.11 -14.09                                                                             .00  .00  -1.40                                                                              -21.25                            8   .850 6.98 -13.11                                                                             4.92 -14.48                                                                             1.52 -18.11                                                                             .00  .00                               __________________________________________________________________________     Condition Corresponding Values: K.sub.aO /γ.sub.aO = 3.80, K.sub.aR     /γ.sub.aR = 0.43                                                   

As can be seen from Tables 6, 7, and 8 above, when a change inconversion coefficient K_(a) : (rs) (e.g., the fourth column in thefirst table) and a change in correction coefficient μ: (l) (e.g., thefourth column in the second table) at a given lens arrangement (e.g., atthe infinity in-focus arrangement) are considered, the conversioncoefficient K_(a) and the correction coefficient μ considerably changedepending on the object positions. In particular, the conversioncoefficient K_(a) has a larger value at the closest object side thanthat at the infinity object side. Since the conversion coefficient K_(a)in the direction of rotation is defined by K_(a) =ΔBf/Δa, the amount Δaof rotation for focusing at the infinity object side becomes larger thanthat at the closest object side relative to the defocus amount ΔBf.

The calculation results of the rate of change of K_(a) with respect toγ_(a) at the infinity in-focus arrangement and the closest in-focusarrangement at the wide-angle end (F=36.0), middle position (F=50.0),and telephoto end (F=103.0) in the embodiment of Japanese PatentApplication Laid-Open No. 5-142475 are as follows.

    ______________________________________                                        Embodiment of Japanese Patent Application Laid-Open No. 5-142475                       Infinity Arrangement                                                                       Closest Arrangement                                              K.sub.aO /γ.sub.aO                                                                   K.sub.aR /γ.sub.aR                                ______________________________________                                        Wide-angle End                                                                           2.75           0.44                                                (F = 36.0)                                                                    Middle Position                                                                          3.36           0.43                                                (F = 50.0)                                                                    Telephoto End                                                                            3.80           0.43                                                (F = 103.0)                                                                   ______________________________________                                    

As described above, in the embodiment of Japanese Patent ApplicationLaid-Open No. 5-142475, since the change in conversion coefficient K_(a)is large, the contribution of the correction term (ΔBf/μ) in K_(a)=γ_(a) (1-ΔBf/μ) becomes large, and the value of the correctioncoefficient μ becomes close to that of the defocus amount ΔBf. Inaddition, the value of the correction coefficient μ largely changesdepending on the object positions.

Therefore, as described in Japanese Patent Application Laid-Open No.3-228006, under the condition that only a pair of a conversioncoefficient γ_(a) value and a correction coefficient μ value are set fora given lens arrangement range (e.g., an infinity in-focus arrangementrange), if the correction coefficient μ which changes largely isrepresented by only one value, a large error is included in the value ofthe conversion coefficient K_(a) which is calculated from the conversioncoefficient γ_(a) and the correction coefficient μ. Therefore, when thelens driving amount Δa for focusing is finally calculated from thedefocus amount ΔBf using the conversion coefficient K_(a), the lensdriving amount includes an error, and an auto-focus operation cannot beaccurately performed.

For example, upon calculation of the lens driving amount Δa for focusingwith respect to a closest distance (R=0.85 m) object when the correctioncoefficient μ (which changes from -3.76 to -5.77 depending on the objectdistances) at the infinity in-focus arrangement at the telephoto end(F=103.0) is represented by the value (μ=-4.82) at the middle objectdistance (R=2.0 m), the lens driving amount Δa for focusing iscalculated as Δa=8.74 by substituting ΔBf=16.18, γ_(a) =0.425, andμ=-4.82. The actual lens driving amount for focusing from the state ofthe infinity in-focus arrangement at the telephoto end (F=103.0) to theclosest distance (R=0.85 m) object is Δa=10.0 from (R, ANGLE)=(0.85,10.0) in the upper right portion of the third table in Table 8.Therefore, an error as large as -12.6% is produced between the actualvalue and the calculated value Δa=8.74 of the lens driving amount forfocusing.

Similarly, when the lens driving amounts upon focusing from the infinityin focus lens arrangement to the closest distance object and uponfocusing from the closest in-focus lens arrangement to the infinityobject at the wide-angle end, middle position, and telephoto end arecalculated from Δa=ΔBf/ γ_(a) (1-ΔBf/μ)!, and errors from the actuallens driving amounts are then calculated, the following large values areobtained.

    ______________________________________                                        Embodiment of Japanese Patent Application Laid-Open No. 5-142475                      Infinity Arrangement →                                                              Closest Arrangement →                                     Closest In-focus State                                                                     Infinity In-focus State                                  ______________________________________                                        Wide-angle End                                                                          -4.4%          -13.0%                                               (F = 36.0)                                                                    Middle Position                                                                         -11.8%         -12.0%                                               (F = 50.0)                                                                    Telephoto End                                                                           -12.6%         -14.6%                                               (F = 103.0)                                                                   ______________________________________                                    

Note that the value of the correction coefficient μ upon focusing fromthe infinity in-focus lens arrangement to the closest distance objectadopts a value at the object distance (R=2.0 m), and the value of thecorrection coefficient μ upon focusing from the closest in-focus lensarrangement to the infinity object adopts a value at the object distance(R=3.0 m).

Finally, Table 9 summarizes the amount (ANGLE DA) of rotation forfocusing upon manual focusing using the focus cam (the middle table inTable 1) of the embodiment of Japanese Patent Application Laid-Open No.5-142475, the amount DX (mm) of movement, in the direction of theoptical axis, of the focusing lens unit corresponding to the amount ofrotation for focusing, and a displacement amount Bf (mm) of the imagingpoint when the amount (DX) of movement in the direction of the opticalaxis is given.

The upper table in Table 9 summarizes the displacement amount (Bf) ofthe imaging point corresponding to the photographing distances (R=5.0,3.0, 2.0, 1.5, 1.0, and 0.85 m) in the respective zooming states of thefocal lengths (F=36.0, 50.0, 60.0, 70.0, 85.0, and 103.0 mm), and themiddle table summarizes the values of the amount (ANGLE DA) of rotationfor focusing required for attaining an optimal in-focus state withrespect to the respective photographing distances. The lower tablesummarizes the amounts (DX) of movement, in the direction of the opticalaxis, of the respective lens units corresponding to the amount (ANGLEDA) of rotation for focusing in association with the focal lengths andthe photographing distances. In the lower table, (F) is the focal length(mm) of the entire system, (R) is the photographing distance (m), and(DX) is the amount (mm) of movement, in the direction of the opticalaxis, of each of the first, second, third, and fourth lens units in turnfrom the right side (movement toward the object side is represented by apositive value).

                                      TABLE 9                                     __________________________________________________________________________    Displacement Amount Bf (mm) of Imaging Point and Amount DX                    (mm) of movement for focusing in Embodiment of Japanese Patent                Application Laid-Open No. 5-142475                                                      0.85 m                                                                             1.00 m                                                                             1.50 m                                                                             2.00 m                                                                             3.00 m                                                                             5.00 m                                     __________________________________________________________________________    F   36.000 Bf                                                                           .000 .000 .000 .000 .000 .000                                       F   50.000 Bf                                                                           .000 .012 .015 .005 .000 -.001                                      F   60.000 Bf                                                                           .000 .005 .022 .017 -.001                                                                              -.007                                      F   70.000 Bf                                                                           .000 -.006                                                                              .001 .010 .008 -.007                                      F   85.000 Bf                                                                           .000 -.015                                                                              -.024                                                                              -.024                                                                              -.010                                                                              .005                                       F  103.000 Bf                                                                           .000 .000 .000 .000 .000 .000                                          ANGLE DA                                                                             10.000                                                                             9.192                                                                              7.365                                                                              6.225                                                                              4.821                                                                              3.379                                      __________________________________________________________________________    F  36.000 DX                                                                            .000   1.037                                                                            .000   .000 R                                                                            0.85 m                                         F  50.000 DX                                                                            .000   1.483                                                                            .000   .000 R                                                                            0.85 m                                         F  60.000 DX                                                                            .000   1.872                                                                            .000   .000 R                                                                            0.85 m                                         F  70.000 DX                                                                            .000   2.311                                                                            .000   .000 R                                                                            0.85 m                                         F  85.000 DX                                                                            .000   3.049                                                                            .000   .000 R                                                                            0.85 m                                         F  103.000 DX                                                                           .000   4.080                                                                            .000   .000 R                                                                            0.85 m                                         F  36.000 DX                                                                            .000   .875                                                                             .000   .000 R                                                                            1.00 m                                         F  50.000 DX                                                                            .000   1.255                                                                            .000   .000 R                                                                            1.00 m                                         F  60.000 DX                                                                            .000   1.599                                                                            .000   .000 R                                                                            1.00 m                                         F  70.000 DX                                                                            .000   1.993                                                                            .000   .000 R                                                                            1.00 m                                         F  85.000 DX                                                                            .000   2.661                                                                            .000   .000 R                                                                            1.00 m                                         F  103.000 DX                                                                           .000   3.609                                                                            .000   .000 R                                                                            1.00 m                                         F  36.000 DX                                                                            .000   .576                                                                             .000   .000 R                                                                            1.50 m                                         F  50.000 DX                                                                            .000   .834                                                                             .000   .000 R                                                                            1.50 m                                         F  60.000 DX                                                                            .000   1.072                                                                            .000   .000 R                                                                            1.50 m                                         F  70.000 DX                                                                            .000   1.365                                                                            .000   .000 R                                                                            1.50 m                                         F  85.000 DX                                                                            .000   1.879                                                                            .000   .000 R                                                                            1.50 m                                         F  103.000 DX                                                                           .000   2.636                                                                            .000   .000 R                                                                            1.50 m                                         F  36.000 DX                                                                            .000   .429                                                                             .000   .000 R                                                                            2.00 m                                         F  50.000 DX                                                                            .000   .629                                                                             .000   .000 R                                                                            2.00 m                                         F  60.000 DX                                                                            .000   .810                                                                             .000   .000 R                                                                            2.00 m                                         F  70.000 DX                                                                            .000   1.037                                                                            .000   .000 R                                                                            2.00 m                                         F  85.000 DX                                                                            .000   1.457                                                                            .000   .000 R                                                                            2.00 m                                         F  103.000 DX                                                                           .000   2.090                                                                            .000   .000 R                                                                            2.00 m                                         F  36.000 DX                                                                            .000   .285                                                                             .000   .000 R                                                                            3.00 m                                         F  50.000 DX                                                                            .000   .422                                                                             .000   .000 R                                                                            3.00 m                                         F  60.000 DX                                                                            .000   .551                                                                             .000   .000 R                                                                            3.00 m                                         F  70.000 DX                                                                            .000   .703                                                                             .000   .000 R                                                                            3.00 m                                         F  85.000 DX                                                                            .000   1.004                                                                            .000   .000 R                                                                            3.00 m                                         F  103.000 DX                                                                           .000   1.488                                                                            .000   .000 R                                                                            3.00 m                                         F  36.000 DX                                                                            .000   .170                                                                             .000   .000 R                                                                            5.00 m                                         F  50.000 DX                                                                            .000   .254                                                                             .000   .000 R                                                                            5.00 m                                         F  60.000 DX                                                                            .000   .336                                                                             .000   .000 R                                                                            5.00 m                                         F  70.000 DX                                                                            .000   .434                                                                             .000   .000 R                                                                            5.00 m                                         F  85.000 DX                                                                            .000   .618                                                                             .000   .000 R                                                                            5.00 m                                         F  103.000 DX                                                                           .000   .951                                                                             .000   .000 R                                                                            5.00 m                                         __________________________________________________________________________

SUMMARY OF THE INVENTION

It is, therefore, an object of the present invention to provide a zoomlens which can suppress changes in conversion coefficient γ_(a) andcorrection coefficient μ above even when the focus cam is used forachieving manual focusing, can suppress the storage capacity by reducingthe number of data of the conversion coefficient γ_(a) and correctioncoefficient μ to be stored in the storage means, can eliminate an errorupon calculation of the lens driving amount Δa for focusing from thedefocus amount ΔBf using the conversion coefficient K_(a) and canachieve accurate auto-focusing.

According to the present invention, in a zoom lens system in which themovement locus of a focusing lens unit is defined by synthesizing afocus cam and a zoom compensation cam so as to achieve an in-focus stateby a substantially constant amount of rotation for an identical objectdistance independently of a zooming state upon expression of apredetermined movement locus for zooming by the amount of movement, inthe direction of the optical axis, of lens units, and the angle ofrotation of a rotatable lens barrel, when the ratios (dBf/dx) of theamount dBf of infinitesimal movement of the imaging plane to the amountdx of infinitesimal movement, in the direction of the optical axis, ofthe focusing lens unit at the infinity and closest in-focus points arerespectively represented by γ_(XO) and γ_(XR), the amounts of movement,in the direction of the optical axis, of the focusing lens unit requiredfor focusing from the infinity position to the closest distance positionat the wide-angle end and the telephoto end are respectively representedby ΔX_(WR) and Δx_(TR) and the amount of rotation of the focusing lensunit on the focus cam corresponding to zooming from the wide-angle endto the telephoto end and the amount of rotation corresponding tofocusing from the infinity in-focus state to the closest in-focus stateare respectively represented by a_(Z) and a_(F), the zoom lens satisfiesconditional formulas (1), (2), and (3) below at least at the telephotoend:

    1.00<γ.sub.XR /γ.sub.XO                        ( 1)

    4.00<ΔX.sub.TR /ΔX.sub.WR <6.00                (2)

    -0.70<a.sub.F /a.sub.Z <-0.50                              (3)

On the other hand, when the ratios (dBf/da) of the amount dBf ofinfinitesimal movement of the imaging plane with respect to the angle daof infinitesimal rotation of the focusing lens unit on the focus cam atthe infinity and closest in-focus points are respectively represented byγ_(aO) and γ_(aR), the zoom lens satisfies the following formula atleast at the wide-angle end and the telephoto end:

    0.25<γ.sub.aR /γ.sub.aO <0.75

Furthermore, when the conversion coefficients K_(a), which are used whenthe focusing lens unit are located at the lens arrangementscorresponding to the infinity and closest in-focus states and areexpressed by K_(a) =ΔBf/Δa, are respectively represented by K_(aO) andK_(aR), the zoom lens satisfies the following formulas at least at thewide-angle end and the telephoto end:

    0.60<K.sub.aO /γ.sub.aO <1.20

    0.80<K.sub.aR /γ.sub.aR <1.70

where

ΔBf: the defocus amount between the imaging position of an object at anarbitrary position and a predetermined imaging point position

Δa: the angle of rotation of the focusing lens unit on the focus camrequired for attaining an in-focus state on the object

As in the above-mentioned first aspect of the present invention, in thethird aspect of the present invention, since the above-mentionedconditional formulas are satisfied, even when the focus cam is used toachieve so-called manual focusing, changes in conversion coefficientγ_(a) and correction coefficient μ required for realizing accurateauto-focusing can be reduced. For this reason, the number of data of theconversion coefficient γ_(a) and correction coefficient μ to be storedin the storage means can be reduced. Furthermore, since the change incorrection coefficient μ is small, an error upon calculation of the lensdriving amount Δa for focusing from the defocus amount ΔBf using theconversion coefficient K_(a) is small, and accurate auto-focusing can berealized.

As described above, when the zoom lens system is constituted by n lensunits, and its k-th lens unit is used as a focusing lens unit, theconversion coefficient γ_(x) associated with the direction of theoptical axis of the focusing lens unit (the ratio dBf/dx of the amountdBf of infinitesimal movement of the imaging plane to the amount dx ofinfinitesimal movement in the direction of the optical axis) isexpressed using the imaging magnifications β of the respective lensunits as follows:

    γ.sub.x =(1-β.sub.k.sup.2)β.sub.k+1.sup.2 β.sub.k+2.sup.2 . . . β.sub.n.sup.2

Therefore, the rate of change, from the infinity in-focus value (γ_(xO))to the closest in-focus value (γ_(xR)), of the conversion coefficientγ_(x) associated with the direction of the optical axis can be expressedusing the imaging magnifications β_(ok) and β_(Rk) of the focusing lensunit at the infinity and closest in-focus points as follows:

    γ.sub.xR /γ.sub.xO =(1-β.sub.Rk.sup.2)/(1-β.sub.Ok.sup.2)

On the other hand, the conversion coefficient γ_(a) associated with thedirection of rotation of the focusing lens unit (the ratio dBf/da of theamount dBf of infinitesimal movement of the imaging plane to the angleda of infinitesimal rotation) can be expressed by:

    γ.sub.a =γ.sub.x.(dx/da)

where dx/da is the slope of the focus cam. For this reason, the rate ofchange, from the infinity in-focus value (γ_(aO)) to the closestin-focus value (γ_(aR)), of the conversion coefficient γ_(a) associatedwith the direction of rotation of the focusing lens unit can beexpressed using slopes (dx/da)_(O) and (dx/da)_(R) at the infinity andclosest corresponding positions on the focus cam as follows:

    γ.sub.aR /γ.sub.aO =(γ.sub.xR /γ.sub.xO).((dx/da).sub.R /(dx/da).sub.O)

Therefore, like in the present invention, in the zoom lens system inwhich the value of the conversion coefficient γ_(X) associated with theamount x of movement, in the direction of the optical axis, of thefocusing lens unit in the closest in-focus state becomes larger thanthat in the infinity in-focus state (1.0<γ_(xR) /γ_(xO)), the ratio ofthe amount a_(F) of rotation of the focusing lens unit on the focus camcorresponding to focusing from the infinity in-focus state to theclosest in-focus state and the amount a_(Z) of rotation corresponding tozooming from the wide-angle end to the telephoto end is set to benegative (a_(F) /a_(Z) <0), so that the focus cam can have a shape inwhich the slope (dx/da) at the closest corresponding position becomessmaller than that at the infinity corresponding position (0<(dx/da)_(R)/(dx/da)_(O) <1.0), thereby reducing the change in conversioncoefficient γ_(a) associated with the direction of rotation.

More specifically, since the rate of change (γ_(aR) /γ_(aO)) from theinfinity in-focus value (γ_(aO)) to the closest in-focus value (γ_(aR)),of the conversion coefficient γ_(a) associated with the direction ofrotation is expressed as a product of the rate of change (γ_(xR)/γ_(xO)) of the conversion ratio γ_(x) associated with the direction ofthe optical axis and the slope ratio (dx/da)_(R) /(dx/da)_(O) of thefocus cam, as described above, the final rate of change (γ_(aR) /γ_(aO))of the conversion coefficient γ_(a) associated with the direction ofrotation can be compressed by adopting an arrangement in which the twochanges cancel out each other.

According to the present invention, in a zoom lens in which theconversion coefficients γ_(x) associated with the amount x of movement,in the direction of the optical axis, of the focusing lens unit at theinfinity and closest in-focus points at the telephoto end satisfiesconditional formula (1):

    1.00<γ.sub.xR /γ.sub.xO                        ( 1)

when the ratio between the amounts ΔX_(WR) and ΔX_(TR) of movement, inthe direction of the optical axis, of the focusing lens unit requiredfor focusing from the infinity position to the closest distance positionat the wide-angle end and the telephoto end satisfies conditionalformula (2):

    4.00<Δx.sub.TR /Δx.sub.WR <6.00                (2)

the ratio of the amount a_(F) of rotation of the focusing lens unit onthe focus cam corresponding to focusing from the infinity in-focus stateto the closest in-focus state to the amount a_(z) of rotationcorresponding to zooming from the wide-angle end to the telephoto end isset to satisfy conditional formula (3):

    -0.70<a.sub.F /a.sub.Z <-0.50                              (3)

Under these conditions, the final rate of change (γ_(aR) /γ_(aO)) of theconversion coefficient γ_(a) associated with the direction of rotationcan be set to be a small value which satisfies conditional formula (4)below:

    0.25<γ.sub.aR /γ.sub.aO <0.75                  (4)

As described above, since the change in conversion coefficient γ_(a) canbe reduced as compared to that in the conventional system, the number ofdata of the conversion coefficient γ_(a) and the correction coefficientμ to be stored in the storage means can be reduced.

For example, upon division of the focus range like in formula (a)(N>log(γ_(MAX) /γ_(MIN))/log(1.2)) above, the following relation issatisfied:

    1.6<log(γ.sub.MAX γ.sub.MIN)/log(1.2)<7.6

and the number of divisions can be smaller than in the conventionalsystem. Therefore, cost can be reduced in terms of the storage capacity.Furthermore, as will be described later in the following description ofthe embodiments, since the changes in conversion coefficient K_(a) andcorrection coefficient μ are smaller than those in the conventionalsystem, an error obtained upon calculation of the lens driving amount Δafor focusing from the defocus amount ABf using the conversioncoefficient K_(a) is small, and an accurate auto-focusing operation canbe realized.

The conditional formulas of the present invention will be explainedbelow.

Conditional formula (1) is associated with the focusing lens unit in thezoom lens according to the present invention. When γ_(xR) /γ_(xO) issmaller than the lower limit of conditional formula (1) (γ_(xR) /γ_(xO)<1.0), the conversion coefficient γ_(x) associated with the direction ofthe optical axis in the closest in-focus state becomes smaller than thatin the infinity in-focus state. For this reason, when the focus cam(0<(dx/da)_(R) /(dx/da)_(O) <1.0) according to the present invention isused, the rate of change of the conversion coefficient γ_(a) associatedwith the direction of rotation, which rate is expressed as a product ofthe rate of change (γ_(xR) /γ_(xO)) of the conversion coefficient γ_(x)associated with the direction of the optical axis and the slope ratio((dx/da)_(R) /(dx/da)_(O)) of the focus cam, becomes excessively smallerthan 1.0 (γ_(aR) /γ_(aO) >>1.0), and changes in γ_(a) become large. As aresult, the number of data of the conversion coefficient γ_(a) and thecorrection coefficient μ to be stored in the storage means increases. Inaddition, since the changes in conversion coefficient K_(a) andcorrection coefficient μ become large, the error obtained uponcalculation of the lens driving amount Δa from the defocus amount ΔBf islarge, and an accurate auto-focusing operation cannot be performed.

Conditional formula (2) is associated with the ratio between the amountsof movement, in the direction of the optical axis, of the focusing lensunit required for focusing from the infinity position to the closestdistance position at the wide--angle end and the telephoto end. As willbe described later in the description of the embodiments, this ratio isan amount which is associated with the ratio of the slope (dx/da)_(R) atthe closest corresponding position to the slope (dx/da)_(o) at theinfinity corresponding position on the focus cam. As the ratio betweenthe two amounts of movement becomes smaller, changes in slope on thefocus cam become smaller. On the contrary, as the ratio between the twoamounts of movement becomes larger, changes in slope on the focus cambecome larger. Therefore, when the ratio is smaller than the lower limitof conditional formula (2), changes in conversion coefficient γ_(a)associated with the direction of rotation become small. However, in thezoom lens of the present invention, which satisfies conditional formula(1), the optimal ratio of the amount a_(F) of rotation of the focusinglens unit on the focus cam corresponding to focusing from the infinityin-focus state to the closest in-focus state to the amount a_(Z) ofrotation corresponding to zooming from the wide-angle end to thetelephoto end falls outside a range defined by conditional formula (3).Therefore, it is more preferable to set the upper limit of conditionalformula (2) to 4.30. On the other hand, when the ratio exceeds the upperlimit of conditional formula (2), since changes in slope on the focuscam become too large as compared to those in conversion coefficientγ_(x) associated with the direction of the optical axis, changes inconversion coefficient γ_(a) associated with the direction of rotationbecome large, and the number of data of the conversion coefficient γ_(a)and the correction coefficient μ to be stored in the storage meansincreases. In addition, an accurate auto-focusing operation cannot beperformed. Conditional formula (3) defines an appropriate ratio of theamount a_(F) of rotation of the focusing lens unit on the focus camcorresponding to focusing from the infinity in-focus state to theclosest in-focus state to the amount a_(Z) of rotation corresponding tozooming from the wide-angle end to the telephoto end. When the ratio issmaller than the lower limit of conditional formula (3), the slope(dx/da) of the focus cam considerably decreases at the closestcorresponding position as compared to the slope at the infinitycorresponding position, and they have a ratio:

     <(dx/da).sub.R /(dx/da).sub.O <<1.0

For this reason, the rate of change of the conversion coefficient γ_(a)associated with the direction of rotation, which rate is expressed as aproduct of the rate of change (γ_(xR) /γ_(xO)) of the conversioncoefficient γ_(x) associated with the direction of the optical axis andthe slope ratio ((dx/da)_(R) /(dx/da)_(O)) of the focus cam, becomesexcessively smaller than 1.0 (γ_(aR) /γ_(aO) <<1.0), and changes inγ_(a) become large. As a result, the number of data of the conversioncoefficient γ_(a) and the correction coefficient μ to be stored in thestorage means increases. In addition, since changes in μ are large, anerror obtained upon calculation of the lens driving amount Δa from thedefocus amount ΔBf is large, and an accurate auto-focusing operationcannot be performed. Therefore, it is more preferable to set the lowerlimit of conditional formula (3) to -0.68.

On the contrary, when the ratio exceeds the upper limit of conditionalformula (3), since the rate of change (γ_(aR) /γ_(aO)) of the conversioncoefficient γ_(a) becomes closer to 1.0, changes in γ_(a) become small,and the number of data of the conversion coefficient γ_(a) and thecorrection coefficient μ to be stored in the storage means can bereduced. However, since the amount aF of rotation for focusing becomessmall relative to the amount a_(z) of rotation corresponding to zoomingfrom the wide-angle end to the telephoto end, the amount of rotation forso-called manual focusing becomes small, and it becomes difficult tomanually attain accurate focusing. Therefore, it is more preferable toset the lower limit of conditional formula (3) to -0.52.

Conditional formula (4) is a condition associated with the number ofdata of the conversion coefficient γ_(a) and the correction coefficientμ to be stored in the storage means, i.e., the number of divisions ofthe focus range. When γ_(aR) /γ_(aO) is smaller than the lower limit ofconditional formula (4), the rate of change (γ_(aR) /γ_(aO)) of theconversion coefficient γ_(a) becomes excessively smaller than 1.0, andchanges in γ_(a) become large. As a result, since the number of data ofthe conversion coefficient γ_(a) and the correction coefficient μ to bestored in the storage means increases, a storage means with a largestorage capacity is required, resulting in an increase in cost.

On the contrary, when γ_(aR) /γ_(aO) exceeds the upper limit ofconditional formula (4), since the rate of change (γ_(aR) /γ_(aO)) ofthe conversion coefficient γ_(a) becomes closer to 1.0, changes in γ_(a)become small, and the number of data of the conversion coefficient γ_(a)and the correction coefficient μ to be stored in the storage means canbe reduced. However, since the conversion coefficient γ_(a) must have aconsiderably large value, the sensitivity (dBf/da) associated with themovement in the direction of rotation becomes strict, and a change inimaging point caused by a slight error factor in the direction ofrotation becomes large, thus disturbing accurate auto-focusing.

Furthermore, in order to attain accurate auto-focusing while loweringthe sensitivity (dBf/da) associated with the movement in the directionof rotation, the upper and lower limits of conditional formula (4) arepreferably set as follows:

    0.28<γ.sub.aR /γ.sub.aO <0.65

In order to obtain a zoom lens which can perform auto-focusing moreaccurately, when the conversion coefficients K_(a) (=ΔBf/Δa) used whenthe focusing lens unit is located at the lens arrangements correspondingto the infinity in-focus state and the closest in-focus state arerespectively represented by K_(aO) and K_(aR), the zoom lens preferablysatisfies conditional formulas (5) and (6) below at least at thewide-angle end and the telephoto end:

    0.60<K.sub.aO /γ.sub.aO <1.20                        (5)

    0.80<K.sub.aR /γ.sub.aR <1.70                        (6)

Conditional formula (5) defines the rate of change of the conversioncoefficient K_(a) in the direction of rotation upon a change in objectposition when the focusing lens unit corresponds to an arrangement inthe infinity in-focus state. When the rate is smaller than the lowerlimit of conditional formula (5), the change in conversion coefficientK_(aO) upon a change in object position becomes too small as compared tothe conversion coefficient γ_(aO) as the sensitivity associated with themovement in the direction of rotation of the focusing lens unit at theinfinity in-focus point. Therefore, for example, when the conversioncoefficient K_(aO) which changes upon a change in object position isexpressed by a pair of a conversion coefficient γ_(aO) value and acorrection coefficient μ_(aO) value on the basis of the relationshipK_(aO) =γ_(aO) (1-ΔBf/μ_(aO)), a large error is produced in the value ofthe conversion coefficient K_(aO) calculated from the conversioncoefficient γ_(aO) and the correction coefficient μ_(aO), thusdisturbing accurate auto-focusing.

On the contrary, when the rate exceeds the upper limit of conditionalformula (5), the change in conversion coefficient K_(aO) in thedirection of rotation upon a change in object position becomes large ascompared to the conversion coefficient γ_(aO) in the direction ofrotation of the focusing lens unit at the infinity in-focus point. Forthis reason, when the conversion coefficient K_(aO) which changes upon achange in object position is expressed by a pair of a conversioncoefficient γ_(aO) value and a correction coefficient μ_(aO) value, alarge error is produced in the value of the conversion coefficientK_(aO) calculated from the conversion coefficient and the correctioncoefficient μ_(aO).

In order to achieve auto-focusing more accurately, the upper and lowerlimits of conditional formula (5) are preferably set as follows:

    0.65<K.sub.aO /γ.sub.aO <1.10

Similarly, when the conversion coefficient K_(aO) changes from (K_(aO)/γ_(aO) <1) to (K_(aO) /γ_(aO) >1) upon a change in object position whenthe focusing lens unit corresponds to an arrangement in the infinityin-focus state, the sign of the correction coefficient Pao changesbefore and after (K_(aO) /γ_(aO) =1). As a result, when the conversioncoefficient K_(ao) is expressed by a pair of a conversion coefficientγ_(a0) value and a correction coefficient μ_(a) value, a large error isproduced in the value of the conversion coefficient K_(aO) calculatedfrom the conversion coefficient γ_(aO) and the correction coefficientμ_(aO). Therefore, the conversion coefficient K_(aO) does not preferablychange too much after it exceeds (K_(aO) /γ_(aO) =1).

Therefore, even when the conversion coefficient K_(aO) changes from(K_(aO) /γ_(aO) <1) to (K_(aO) /γ_(aO) >1), the zoom lens preferablysatisfies the following conditional formula:

    0.65 <K.sub.aO /γ.sub.aO <1.10

Conditional formula (6) defines the rate of change of the conversioncoefficient K_(a) in the direction of rotation upon a change in objectposition when the focusing lens unit corresponds to an arrangement inthe closest in-focus position. When the rate exceeds the upper limit ofconditional formula (6), the change in conversion coefficient K_(aR) inthe direction of rotation upon a change in object position becomes toolarge as compared to the conversion coefficient γ_(aR) as thesensitivity associated with the movement in the direction of rotation ofthe focusing lens unit at the closest in-focus point. Therefore, forexample, when the conversion coefficient K_(aR) which changes upon achange in object position is expressed by a pair of a conversioncoefficient γ_(aR) value and a correction coefficient μ_(aR) value onthe basis of the relationship K_(aR) =γ_(aR) (1-ΔBf/μ_(aR)), a largeerror is produced in the value of the conversion coefficient KaRcalculated from the conversion coefficient γ_(aR) and the correctioncoefficient μ_(aR) thus disturbing accurate auto-focusing.

On the contrary, when the rate is smaller than the lower limit ofconditional formula (6), the change in conversion coefficient K_(aR) inthe direction of rotation upon a change in object position becomes smallas compared to the conversion coefficient γ_(aR) in the direction ofrotation of the focusing lens unit at the closest in-focus point. Forthis reason, when the conversion coefficient K_(aR) which changes upon achange in object position is expressed by a pair of a conversioncoefficient γ_(aR) value and a correction coefficient μ_(aR) value, alarge error is produced in the value of the conversion coefficientK_(aR) calculated from the conversion coefficient γ_(aR) and thecorrection coefficient μ_(aR).

In order to achieve auto-focusing more accurately, the upper and lowerlimits of conditional formula (6) are preferably set as follows:

    0.90<K.sub.aR /γ.sub.aR <1.55

Similarly, when the conversion coefficient K_(aR) changes from (K_(aR)/γ_(aR) <1) to (K_(aR) /γ_(aR) >1) upon a change in object position whenthe focusing lens unit corresponds to an arrangement in the closestin-focus state, the sign of the correction coefficient μ_(aR) changesbefore and after (K_(aR) /γ_(aR) =1). As a result, when the conversioncoefficient K_(aR) is expressed by a pair of a conversion coefficientγ_(aR) value and a correction coefficient μ_(aR) value, a large error isproduced in the value of the conversion coefficient K_(aR) calculatedfrom the conversion coefficient γ_(aR) and the correction coefficientμ_(aR). Therefore, the conversion coefficient K_(aR) preferably does notchange too much after it exceeds (K_(aR) /γ_(aR) =1).

Therefore, even when the conversion coefficient K_(aR) changes from(K_(aR) /γ_(aR) <1) to (K_(aR) /γ_(aR) >1), the zoom lens preferablysatisfies the following conditional formula:

    0.90>K.sub.aR /γ.sub.aR >1.55

The above and other objects, features and advantages of the presentinvention are explained hereinafter and may be better understood byreference to the drawings and the descriptive matter which follows.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a view showing the movement loci for zooming of a zoom lensaccording to the first embodiment of the present invention;

FIG. 1B is a view showing the shapes of a focus cam and a zoomcompensation cam of a second lens unit in the zoom lens according to thefirst embodiment of the present invention; and

FIG. 2 is a view for explaining the shape of the focus cam in the zoomlens according to the first embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will be described in detail hereinafter withreference to its embodiments.

First Embodiment!

A zoom lens of the first embodiment is a zoom lens which has a four-unitarrangement, i.e., positive, negative, positive, and positive lensunits, and attains focusing by a negative second lens unit. In this zoomlens, the rotation amount ratio (a_(F) /a_(Z)) of the rotation amountfor focusing from the infinity in-focus position to the closest in-focusposition (R=0.8 m) to the amount of rotation for zooming from thewide-angle end (F=36.0) to the telephoto end (F=131.0) is set to be-0.55.

Table 10 below summarizes various paraxial data of an optical system anddata for defining the shape of a focus cam according to the firstembodiment.

The upper table in Table 10 summarizes the focal length data, and theprincipal point interval data relating to six zooming states (F=36.0(1-POS), 50.0 (2-POS), 70.0 (3-POS), 85.0 (4-POS), 105.0 (5-POS), and131.0 mm (6-POS)) of the respective lens units of the optical systemcorresponding to the first embodiment.

In this table, F1, F2, F3, and F4 are respectively the focal lengths offirst, second, third and fourth lens units, and D1, D2, D3, and D4 arerespectively the principal point interval between the first and secondlens units, the principal point interval between the second and thirdlens units, the principal point interval between the third and fourthlens units, and the principal point interval between the fourth lensunit and a predetermined imaging plane in six zooming states (F=36.0,50.0, 70.0, 85.0, 105.0 and 131.0 mm).

The middle table in Table 10 summarizes spline sample data when theshape (a curve g_(2F) in FIG. 1B) of the focus cam in the second lensunit of the first embodiment, which is used for focusing, is expressedby the above-mentioned spline function associated with the angle a ofrotation of a rotatable lens barrel and the amount x of movement in thedirection of the optical axis. In this middle table, (1), (2), (3), and(4) correspond to the first, second, third, and fourth lens units,respectively.

Furthermore, the lower table in Table 10 summarizes the infinityfocusing positions (infinity corresponding positions) at the respectivefocal lengths (F=36.0, 50.0, 70.0, 85.0, 105.0 and 131.0 mm), and theamounts of rotation (amounts of rotation for focusing) upon focusing torespective photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.0, and 0.8m) using the focus cam of the first embodiment. In the lower table inTable 10, since the amount of rotation for zooming from the wide-angleend (F=36.0) to the telephoto end (F=131.0) is set to be 10.0, and theamount of rotation for focusing from the infinity in-focus position tothe closest in-focus position (R=0.8 m) is set to be -5.5, the rotationamount ratio (a_(F) /a_(Z)) of the amount of rotation for focusing tothe amount of rotation for zooming in the first embodiment is

                                      TABLE 10                                    __________________________________________________________________________    First Embodiment f = 36.0 to 131.0 (Rotation Amount Ratio: a.sub.F            /a.sub.Z = -0.55)                                                             __________________________________________________________________________    Focal lengths and Principal Point Intervals of Lens Units of First            Embodiment                                                                               1-POS                                                                             2-POS                                                                              3-POS                                                                             4-POS                                                                              5-POS                                                                              6-POS                                       __________________________________________________________________________            F  36.0000                                                                           50.0000                                                                            70.0000                                                                           85.0000                                                                            105.0000                                                                           131.0000                                    F1 73.0000                                                                            D1 10.4075                                                                           17.8050                                                                            24.9191                                                                           28.6662                                                                            32.4300                                                                            36.0004                                     F2 -16.6000                                                                           D2 25.6151                                                                           21.3295                                                                            17.3824                                                                           15.1421                                                                            12.6290                                                                            9.7969                                      F3 42.0000                                                                            D3 10.0000                                                                           9.2923                                                                             8.2560                                                                            7.6919                                                                             7.2951                                                                             7.2634                                      F4 80.0000                                                                            D4 63.8473                                                                           70.6899                                                                            77.4519                                                                           81.1930                                                                            85.0439                                                                            88.8003                                     __________________________________________________________________________    Focus Cam Shape (Spline Interpolation Sample Point) Corresponding to          First Embodiment                                                                   ANGLE     (1)                                                                              (2)       (3)                                                                              (4)                                            __________________________________________________________________________    1    -10.0000  .0000                                                                            1.5900    .0000                                                                            .0000                                          2    -5.5000   .0000                                                                            1.0414    .0000                                                                            .0000                                          3    -4.0766   .0000                                                                            .8252     .0000                                                                            .0000                                          4    -2.4812   .0000                                                                            .5436     .0000                                                                            .0000                                          5    -1.7845   .0000                                                                            .4054     .0000                                                                            .0000                                          6    -1.1428   .0000                                                                            .2688     .0000                                                                            .0000                                          7    -.6649    .0000                                                                            .1606     .0000                                                                            .0000                                          8    .0000     .0000                                                                            .0000     .0000                                                                            .0000                                          9    4.5000    .0000                                                                            -1.5242   .0000                                                                            .0000                                          10   5.9234    .0000                                                                            -2.2725   .0000                                                                            .0000                                          11   7.5188    .0000                                                                            -3.4200   .0000                                                                            .0000                                          12   8.2155    .0000                                                                            -4.0941   .0000                                                                            .0000                                          13   8.8572    .0000                                                                            -4.8774   .0000                                                                            .0000                                          14   9.3351    .0000                                                                            -5.6291   .0000                                                                            .0000                                          15   10.0000   .0000                                                                            -7.2001   .0000                                                                            .0000                                          16   11.0000   .0000                                                                            -12.0400  .0000                                                                            .0000                                          __________________________________________________________________________    Amount of Rotation for Zooming and Amount of Rotation for Focusing of         First Embodiment                                                              (Rotation Amount Ratio: a.sub.F /a.sub.Z = -0.55)                                     Infinity            Amount of                                                 Corresponding                                                                              Photographing                                                                        Rotation for                                      Focal Length                                                                          Position     Distance                                                                             Focusing                                          __________________________________________________________________________     36.0 mm                                                                              .0000        5.00 m -.665                                              50.0 mm                                                                              3.2755       3.00 m -1.143                                             70.0 mm                                                                              6.2947       2.00 m -1.784                                             85.0 mm                                                                              7.7608       1.50 m -2.481                                            105.0 mm                                                                              9.0631       1.00 m -4.077                                            131.0 mm                                                                              10.0000      0.80 m -5.500                                            __________________________________________________________________________    Condition Corresponding Value (1)                                                                       2.30                                                Condition Corresponding Value (2)                                                                       5.45                                                Condition Corresponding Value (3)                                                                      -0.55                                                Condition Corresponding Value (4)                                                                       0.59 (wide-angle end)                                                         0.31 (telephoto end)                                Condition Corresponding Value (5)                                                                       0.83 (wide-angle end)                                                         0.96 (telephoto end)                                Condition Corresponding Value (6)                                                                       1.23 (wide-angle end)                                                         1.14 (telephoto end)                                __________________________________________________________________________

Table 11 below summarizes the numerical value data of the cams of thefocusing lens unit in the first embodiment, which data are calculated byinterpolation based on a spline function on the basis of the sample dataof the focus cam summarized in the middle table in Table 10. In thistable, (ANGLE) is the angle of rotation of the rotatable lens barrel,(2) is the amount (mm) of movement, in the direction of the opticalaxis, of the second lens unit, and (F) is the focal length (mm) of theentire system in an infinity in-focus state corresponding to the amount(ANGLE) of rotation.

                  TABLE 11                                                        ______________________________________                                        Cam Numerical Value Data of                                                   Focusing Lens Unit in First Embodiment                                        Focus Cam        Zoom Compensation Cam                                        Numerical Value Data                                                                           Numerical Value Data                                         ANGLE (2)      F         ANGLE  (2)    F                                      ______________________________________                                        -5.5000                                                                             1.0414   .0000                                                          -5.0000                                                                             .9689    .0000                                                          -4.5000                                                                             .8927    .0000                                                          -4.0000                                                                             .8127    .0000                                                          -3.5000                                                                             .7287    .0000                                                          -3.0000                                                                             .6403    .0000                                                          -2.5000                                                                             .5472    .0000                                                          -2.0000                                                                             .4493    .0000                                                          -1.5000                                                                             .3460    .0000                                                          -1.0000                                                                             .2371    .0000                                                          -.5000                                                                              .1218    .0000                                                          .0000 .0000    36.0000   .0000  .0000  36.0000                                .5000 -.1280   37.8410   .5000  .4111  37.8410                                1.0000                                                                              -.2632   39.7481   1.0000 .8253  39.7481                                1.5000                                                                              -.4069   41.7511   1.5000 1.2474 41.7511                                2.0000                                                                              -.5604   43.8765   2.0000 1.6811 43.8765                                2.5000                                                                              -.7252   46.1469   2.5000 2.1289 46.1469                                3.0000                                                                              -.9027   48.5819   3.0000 2.5928 48.5819                                3.5000                                                                              -1.0941  51.1974   3.5000 3.0738 51.1974                                4.0000                                                                              -1.3008  54.0062   4.0000 3.5723 54.0062                                4.5000                                                                              -1.5242  57.0169   4.5000 4.0882 57.0169                                5.0000                                                                              -1.7661  60.2406   5.0000 4.6223 60.2406                                5.5000                                                                              -2.0297  63.7319   5.5000 5.1801 63.7319                                6.0000                                                                              -2.3186  67.5623   6.0000 5.7679 67.5623                                6.5000                                                                              -2.6379  71.7931   6.5000 6.3917 71.7931                                7.0000                                                                              -2.9964  76.5442   7.0000 7.0640 76.5442                                7.5000                                                                              -3.4037  81.9189   7.5000 7.7954 81.9189                                8.0000                                                                              -3.8704  88.0195   8.0000 8.5963 88.0195                                8.5000                                                                              -4.4152  95.0681   8.5000 9.4889 95.0681                                9.0000                                                                              -5.0856  103.7508  9.0000 10.5402                                                                              103.7508                               9.5000                                                                              -5.9285  114.5687  9.5000 11.7971                                                                              114.5687                               10.0000                                                                             -7.2001  131.0000  10.0000                                                                              13.5983                                                                              131.0000                               ______________________________________                                    

The left table in Table 11 summarizes the numerical value data of thefocus cam of the first embodiment, and the right table in Table 11summarizes the numerical value data of the zoom compensation cam of thisembodiment. A value obtained by synthesizing the amounts (2) of movementin the direction of the optical axis in the numerical value data of thefocus cam and the zoom compensation cam in the range from the amount ofrotation (ANGLE=0.0) to the amount of rotation (ANGLE=10.0) coincideswith the movement locus (a curve g₂ in FIG. 1A) of the second lens unitcalculated using the paraxial data in the upper table in Table 10.

Therefore, the zoom compensation cam (a curve g_(2H) in FIG. 1B) isdetermined by subtracting the focus cam (the curve g_(2F) in FIG. 1B)from the movement locus (the curve g₂ in FIG. 1A) upon zooming of thesecond lens unit determined by the paraxial data in the upper table inTable 10.

FIGS. 1A and 1B and FIG. 2 will be briefly described below.

FIG. 1A shows the paraxial arrangement and the movement loci uponzooming of the zoom lens according to the first embodiment, and FIG. 1Bshows the shapes of the focus cam and the zoom compensation cam of thesecond lens unit of this embodiment. Referring to FIGS. 1A and 1B, G1,G2, G3, and G4 respectively represent the first, second, third, andfourth lens units, and g₁, g₂, g₃, and g₄ respectively represent themovement loci upon zooming of the first, second, third, and fourth lensunits. In addition, g_(2F), and g_(2H) respectively represent the shapesof the focus cam and the zoom compensation cam of the second lens unit.As described above, a shape obtained by synthesizing the focus camg_(2F) and the zoom compensation cam g_(2H) of the second lens unitcoincides with the movement locus g₂ of the second lens unit.

FIG. 2 is a view for explaining the shape of the focus cam g_(2F) of thefirst embodiment. Referring to FIG. 2, (f=36.0; R=un) and (f=36.0;R=0.80) respectively represent the in-focus positions at the infinityand the closest distance (R=0.80 m) at the wide-angle end, andcoordinate positions (x; a) on the focus cam are respectively (x; a)=(0;0) and (x; a)=(1.041; -5.5). On the other hand, (f=131; R=un) and(f=131; R=0.80) respectively represent the in-focus positions at theinfinity and the closest distance (R=0.80 m) at the telephoto end, andcoordinate positions (x; a) on the focus cam are respectively (x;a)=(-7.200; 10) and (x; a)=(-1.524; 4.5).

Upon zooming from the wide-angle end to the telephoto end, the secondlens unit moves on the focus cam g_(2F) from the coordinate position (0;0) to the coordinate position (-7.200; 10) for an infinity object, andfrom the coordinate position (1.041; -5.5) to the coordinate position(-1.524; 4.5) for a closest distance object. Therefore, the second lensunit moves by 10.0 in the direction of rotation (the direction of anaxis a) in both the cases. On the other hand, upon focusing from theinfinity arrangement to the closest distance object, the second lensunit moves on the focus cam g_(2F) from the coordinate position (0; 0)to the coordinate position (1.041; -5.5) at the wide-angle end, and fromthe coordinate position (-7.200; 10) to the coordinate position (-1.524;4.5) at the telephoto end. Therefore, the second lens unit moves by -5.5in the direction of rotation (the direction of the axis a) at theseends. In contrast to this, in the direction of the optical axis (thedirection of an axis x), the second lens unit moves by 1.041 at thewide-angle end, and by 5.676 at the telephoto end.

Since the shape of the focus cam g_(2F) is determined by interpolatingthe coordinates (f=36.0; R=0.80), (f=36.0; R=un), (f=131; R=0.80), and(f=131; R=un) by the spline function, the change in slope (dx/da) of thefocus cam g_(2F) becomes larger as the absolute value of thex-coordinate of (f=36.0; R=0.80) is smaller or as the absolute value ofthe x-coordinate of (f=131; R=un) is larger. More specifically, as theratio (Δx_(TR) /ΔX_(WR)) between the amounts ΔxTR and ΔXWR of movement,in the direction of the optical axis, of the focusing lens unit requiredfor focusing from the infinity position to the closest distance positionat the wide-angle end or telephoto end is larger, the change in slope(dx/da) of the focus cam becomes larger.

Tables 12, 13, and 14 below summarize the amount DX (mm) of movement forfocusing, in the direction of the optical axis, of the focusing lensunit, the imaging magnifications β_(k) , of the respective lens units,the conversion coefficient γ_(x) associated with the direction of theoptical axis, the slope (dx/da) of the focus cam, and the conversioncoefficient γ_(a) associated with the direction of rotation at thewide-angle end (F=36.0), the middle position (F=70.0), and the telephotoend (F=131.0) according to the first embodiment, respectively. In thesetables, (R) on the left side is the photographing distance (m), (ANG) isthe amount of rotation on the focus cam upon focusing to the respectivephotographing distances, and 1), 2), 3), and 4) on the right siderespectively represent the first, second, third, and fourth lens units.Also, in these tables, the first table summarizes the amount DX (mm) ofmovement for focusing in the direction of the optical axis upon focusingto the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5,1.0, and 0.80 m) (note that movement toward the object side ispositive). The second table summarizes the imaging magnifications β_(k)of the respective lens units in an in-focus state at the respectivephotographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.80 m).The third table summarizes the conversion coefficient γ_(x) associatedwith the direction of the optical axis of the focusing lens unit in anin-focus state at the respective photographing distances (R=10.0, 5.0,3.0, 2.0, 1.5, 1.0, and 0.80 m). Furthermore, the fourth tablesummarizes the slope (dx/da) of the focus cam at the positions, on thefocus cam, corresponding to an in-focus state at the respectivephotographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.80 m),and the fifth table summarizes the conversion coefficient γ_(a)associated with the direction of rotation of the focusing lens unit inan in-focus state at the respective photographing distances (R=10.0,5.0, 3.0, 2.0, 1.5, 1.0, and 0.80 m).

                                      TABLE 12                                    __________________________________________________________________________    Amount DX (mm) of Movement for Focusing in Direction of Optical Axis at       Wide-angle                                                                    End (36.0 mm) in First Embodiment                                             __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) .000                                                                             3) .000                                                                              4) .000                                       R 10.000                                                                            ANG                                                                              -.326                                                                             1) .000                                                                             2) .080                                                                             3) .000                                                                              4) .000                                       R 5.000                                                                             ANG                                                                              -.665                                                                             1) .000                                                                             2) .161                                                                             3) .000                                                                              4) .000                                       R 3.000                                                                             ANG                                                                              -1.143                                                                            1) .000                                                                             2) .269                                                                             3) .000                                                                              4) .000                                       R 2.000                                                                             ANG                                                                              -1.784                                                                            1) .000                                                                             2) .405                                                                             3) .000                                                                              4) .000                                       R 1.500                                                                             ANG                                                                              -2.481                                                                            1) .000                                                                             2) .544                                                                             3) .000                                                                              4) .000                                       R 1.000                                                                             ANG                                                                              -4.077                                                                            1) .000                                                                             2) .825                                                                             3) .000                                                                              4) .000                                       R .800                                                                              ANG                                                                              -5.500                                                                            1) .000                                                                             2) 1.041                                                                            3) .000                                                                              4) .000                                       __________________________________________________________________________    Imaging Magnification β.sub.K of Lens Units at Wide-angle End (36.0      mm) in                                                                        First Embodiment                                                              __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) -.361                                                                            3) -6.767                                                                            4) .202                                       R 10.000                                                                            ANG                                                                              -.326                                                                             1) -.007                                                                            2) -.356                                                                            3) -6.767                                                                            4) .202                                       R 5.000                                                                             ANG                                                                              -.665                                                                             1) -.015                                                                            2) -.351                                                                            3) -6.767                                                                            4) .202                                       R 3.000                                                                             ANG                                                                              -1.143                                                                            1) -.026                                                                            2) -.345                                                                            3) -6.767                                                                            4) .202                                       R 2.000                                                                             ANG                                                                              -1.784                                                                            1) -.040                                                                            2) -.337                                                                            3) -6.767                                                                            4) .202                                       R 1.500                                                                             ANG                                                                              -2.481                                                                            1) -.055                                                                            2) -.328                                                                            3) -6.767                                                                            4) .202                                       R 1.000                                                                             ANG                                                                              -4.077                                                                            1) -.089                                                                            2) -.311                                                                            3) -6.767                                                                            4) .202                                       R .800                                                                              ANG                                                                              -5.500                                                                            1) -.118                                                                            2) -.298                                                                            3) -6.767                                                                            4) .202                                       __________________________________________________________________________    Conversion Coefficient γ.sub.x Associated With Direction of Optical     Axis at Wide-angle End                                                        (36.0 mm) in First Embodiment                                                 __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) 1.624                                                                            3) .000                                                                              4) .000                                       R 10.000                                                                            ANG                                                                              -.326                                                                             1) .000                                                                             2) 1.630                                                                            3) .000                                                                              4) .000                                       R 5.000                                                                             ANG                                                                              -.665                                                                             1) .000                                                                             2) 1.637                                                                            3) .000                                                                              4) .000                                       R 3.000                                                                             ANG                                                                              -1.143                                                                            1) .000                                                                             2) 1.645                                                                            3) .000                                                                              4) .000                                       R 2.000                                                                             ANG                                                                              -1.784                                                                            1) .000                                                                             2) 1.655                                                                            3) .000                                                                              4) .000                                       R 1.500                                                                             ANG                                                                              -2.481                                                                            1) .000                                                                             2) 1.666                                                                            3) .000                                                                              4) .000                                       R 1.000                                                                             ANG                                                                              -4.077                                                                            1) .000                                                                             2) 1.686                                                                            3) .000                                                                              4) .000                                       R .800                                                                              ANG                                                                              -5.500                                                                            1) .000                                                                             2) 1.701                                                                            3) .000                                                                              4) .000                                       __________________________________________________________________________    Slope dx/da of Focus Cam at Wide-angle End (36.0 mm) in First                 __________________________________________________________________________    Embodiment                                                                    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) -.250                                                                            3) .000                                                                              4) .000                                       R 10.000                                                                            ANG                                                                              -.326                                                                             1) .000                                                                             2) -.242                                                                            3) .000                                                                              4) .000                                       R 5.000                                                                             ANG                                                                              -.665                                                                             1) .000                                                                             2) -.233                                                                            3) .000                                                                              4) .000                                       R 3.000                                                                             ANG                                                                              -1.143                                                                            1) .000                                                                             2) -.220                                                                            3) .000                                                                              4) .000                                       R 2.000                                                                             ANG                                                                              -1.784                                                                            1) .000                                                                             2) -.206                                                                            3) .000                                                                              4) .000                                       R 1.500                                                                             ANG                                                                              -2.481                                                                            1) .000                                                                             2) -.191                                                                            3) .000                                                                              4) .000                                       R 1.000                                                                             ANG                                                                              -4.077                                                                            1) .000                                                                             2) -.163                                                                            3) .000                                                                              4) .000                                       R .800                                                                              ANG                                                                              -5.500                                                                            1) .000                                                                             2) -.142                                                                            3) .000                                                                              4) .000                                       __________________________________________________________________________    Conversion Coefficient γ.sub.a Associated With Direction of             Rotation at Wide-angle End                                                    (36.0 mm) in First Embodiment                                                 __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) -.406                                                                            3) .000                                                                              4) .000                                       R 10.000                                                                            ANG                                                                              -.326                                                                             1) .000                                                                             2) -.394                                                                            3) .000                                                                              4) .000                                       R 5.000                                                                             ANG                                                                              -.665                                                                             1) .000                                                                             2) -.381                                                                            3) .000                                                                              4) .000                                       R 3.000                                                                             ANG                                                                              -1.143                                                                            1) .000                                                                             2) -.362                                                                            3) .000                                                                              4) .000                                       R 2.000                                                                             ANG                                                                              -1.784                                                                            1) .000                                                                             2) -.341                                                                            3) .000                                                                              4) .000                                       R 1.500                                                                             ANG                                                                              -2.481                                                                            1) .000                                                                             2) -.319                                                                            3) .000                                                                              4) .000                                       R 1.000                                                                             ANG                                                                              -4.077                                                                            1) .000                                                                             2) -.274                                                                            3) .000                                                                              4) .000                                       R .800                                                                              ANG                                                                              -5.500                                                                            1) .000                                                                             2) -.241                                                                            3) .000                                                                              4) .000                                       __________________________________________________________________________     Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.05,        γ.sub.aR /γ.sub.a0 = 0.59                                    

                                      TABLE 13                                    __________________________________________________________________________    Amount DX (mm) of Movement for Focusing in Direction of Optical Axis at       Middle                                                                        Position (70.0 mm) in First Embodiment                                        __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) .000                                                                              3) .000                                                                              4) .000                                      R 10.000                                                                            ANG                                                                              -.326                                                                             1) .000                                                                             2) .203                                                                              3) .000                                                                              4) .000                                      R 5.000                                                                             ANG                                                                              -.666                                                                             1) .000                                                                             2) .401                                                                              3) .000                                                                              4) .000                                      R 3.000                                                                             ANG                                                                              -1.143                                                                            1) .000                                                                             2) .659                                                                              3) .000                                                                              4) .000                                      R 2.000                                                                             ANG                                                                              -1.782                                                                            1) .000                                                                             2) .972                                                                              3) .000                                                                              4) .000                                      R 1.500                                                                             ANG                                                                              -2.474                                                                            1) .000                                                                             2) 1.278                                                                             3) .000                                                                              4) .000                                      R 1.000                                                                             ANG                                                                              -4.063                                                                            1) .000                                                                             2) 1.867                                                                             3) .000                                                                              4) .000                                      R .800                                                                              ANG                                                                              -5.500                                                                            1) .000                                                                             2) 2.296                                                                             3) .000                                                                              4) .000                                      __________________________________________________________________________    Imaging Magnification β.sub.K of Lens Units at Middle Position (70.0     mm) in First                                                                  Embodiment                                                                    __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) -.527                                                                             3) -57.094                                                                           4) .032                                      R 10.000                                                                            ANG                                                                              -.326                                                                             1) -.007                                                                            2) -.515                                                                             3) -57.094                                                                           4) .032                                      R 5.000                                                                             ANG                                                                              -.666                                                                             1) -.015                                                                            2) -.503                                                                             3) -57.094                                                                           4) .032                                      R 3.000                                                                             ANG                                                                              -1.143                                                                            1) -.026                                                                            2) -.488                                                                             3) -57.094                                                                           4) .032                                      R 2.000                                                                             ANG                                                                              -1.782                                                                            1) -.041                                                                            2) -.469                                                                             3) -57.094                                                                           4) .032                                      R 1.500                                                                             ANG                                                                              -2.474                                                                            1) -.056                                                                            2) -.450                                                                             3) -57.094                                                                           4) .032                                      R 1.000                                                                             ANG                                                                              -4.063                                                                            1) -.091                                                                            2) -.415                                                                             3) -57.094                                                                           4) .032                                      R .800                                                                              ANG                                                                              -5.500                                                                            1) -.122                                                                            2) -.389                                                                             3) -57.094                                                                           4) .032                                      __________________________________________________________________________    Conversion Coefficient γ.sub.x Associated With Direction of Optical     Axis at Middle Position                                                       (70.0 mm) in First Embodiment                                                 __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) 2.387                                                                             3) .000                                                                              4) .000                                      R 10.000                                                                            ANG                                                                              -.326                                                                             1) .000                                                                             2) 2.430                                                                             3) .000                                                                              4) .000                                      R 5.000                                                                             ANG                                                                              -.666                                                                             1) .000                                                                             2) 2.470                                                                             3) .000                                                                              4) .000                                      R 3.000                                                                             ANG                                                                              -1.143                                                                            1) .000                                                                             2) 2.521                                                                             3) .000                                                                              4) .000                                      R 2.000                                                                             ANG                                                                              -1.782                                                                            1) .000                                                                             2) 2.580                                                                             3) .000                                                                              4) .000                                      R 1.500                                                                             ANG                                                                              -2.474                                                                            1) .000                                                                             2) 2.636                                                                             3) .000                                                                              4) .000                                      R 1.000                                                                             ANG                                                                              -4.063                                                                            1) .000                                                                             2) 2.738                                                                             3) .000                                                                              4) .000                                      R .800                                                                              ANG                                                                              -5.500                                                                            1) .000                                                                             2) 2.807                                                                             3) .000                                                                              4) .000                                      __________________________________________________________________________    Slope dx/da of Focus Cam at Middle Position (70.0 mm) in First                __________________________________________________________________________    Embodiment                                                                    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) -.644                                                                             3) .000                                                                              4) .000                                      R 10.000                                                                            ANG                                                                              -.326                                                                             1) .000                                                                             2) -.602                                                                             3) .000                                                                              4) .000                                      R 5.000                                                                             ANG                                                                              -.666                                                                             1) .000                                                                             2) -.565                                                                             3) .000                                                                              4) .000                                      R 3.000                                                                             ANG                                                                              -1.143                                                                            1) .000                                                                             2) -.518                                                                             3) .000                                                                              4) .000                                      R 2.000                                                                             ANG                                                                              -1.782                                                                            1) .000                                                                             2) -.465                                                                             3) .000                                                                              4) .000                                      R 1.500                                                                             ANG                                                                              -2.474                                                                            1) .000                                                                             2) -.418                                                                             3) .000                                                                              4) .000                                      R 1.000                                                                             ANG                                                                              -4.063                                                                            1) .000                                                                             2) -.329                                                                             3) .000                                                                              4) .000                                      R .800                                                                              ANG                                                                              -5.500                                                                            1) .000                                                                             2) -.272                                                                             3) .000                                                                              4) .000                                      __________________________________________________________________________    Conversion Coefficient γ.sub.a Associated With Direction of             Rotation at Middle Position                                                   (70.0 mm) in First Embodiment                                                 __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) -1.538                                                                            3) .000                                                                              4) .000                                      R 10.000                                                                            ANG                                                                              -.326                                                                             1) .000                                                                             2) -1.462                                                                            3) .000                                                                              4) .000                                      R 5.000                                                                             ANG                                                                              -.666                                                                             1) .000                                                                             2) -1.394                                                                            3) .000                                                                              4) .000                                      R 3.000                                                                             ANG                                                                              -1.143                                                                            1) .000                                                                             2) -1.305                                                                            3) .000                                                                              4) .000                                      R 2.000                                                                             ANG                                                                              -1.782                                                                            1) .000                                                                             2) -1.201                                                                            3) .000                                                                              4) .000                                      R 1.500                                                                             ANG                                                                              -2.474                                                                            1) .000                                                                             2) -1.102                                                                            3) .000                                                                              4) .000                                      R 1.000                                                                             ANG                                                                              -4.063                                                                            1) .000                                                                             2) -.900                                                                             3) .000                                                                              4) .000                                      R .800                                                                              ANG                                                                              -5.500                                                                            1) .000                                                                             2) -.762                                                                             3) .000                                                                              4) .000                                      __________________________________________________________________________     Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.18,        γ.sub.aR /γ.sub.a0 = 0.50                                    

                                      TABLE 14                                    __________________________________________________________________________    Amount DX (mm) of Movement for Focusing in Direction of Optical Axis at       Telephoto                                                                     End (131.0 mm) in First Embodiment                                            __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) .000                                                                              3) .000                                                                              4) .000                                      R 10.000                                                                            ANG                                                                              -.315                                                                             1) .000                                                                             2) .884                                                                              3) .000                                                                              4) .000                                      R 5.000                                                                             ANG                                                                              -.665                                                                             1) .000                                                                             2) 1.571                                                                             3) .000                                                                              4) .000                                      R 3.000                                                                             ANG                                                                              -1.143                                                                            1) .000                                                                             2) 2.323                                                                             3) .000                                                                              4) .000                                      R 2.000                                                                             ANG                                                                              -1.784                                                                            1) .000                                                                             2) 3.106                                                                             3) .000                                                                              4) .000                                      R 1.500                                                                             ANG                                                                              -2.481                                                                            1) .000                                                                             2) 3.780                                                                             3) .000                                                                              4) .000                                      R 1.000                                                                             ANG                                                                              -4.077                                                                            1) .000                                                                             2) 4.928                                                                             3) .000                                                                              4) .000                                      R .800                                                                              ANG                                                                              -5.500                                                                            1) .000                                                                             2) 5.676                                                                             3) .000                                                                              4) .000                                      __________________________________________________________________________    Imaging Magnification β.sub.K of Lens Units at Telephoto End (131.0      mm) in First Embodiment                                                       __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) -.814                                                                             3) 20.047                                                                            4) -.110                                     R 10.000                                                                            ANG                                                                              -.315                                                                             1) -.007                                                                            2) -.760                                                                             3) 20.047                                                                            4) -.110                                     R 5.000                                                                             ANG                                                                              -.665                                                                             1) -.015                                                                            2) -.719                                                                             3) 20.047                                                                            4) -.110                                     R 3.000                                                                             ANG                                                                              -1.143                                                                            1) -.026                                                                            2) -.674                                                                             3) 20.047                                                                            4) -.110                                     R 2.000                                                                             ANG                                                                              -1.784                                                                            1) -.041                                                                            2) -.627                                                                             3) 20.047                                                                            4) -.110                                     R 1.500                                                                             ANG                                                                              -2.481                                                                            1) -.057                                                                            2) -.586                                                                             3) 20.047                                                                            4) -.110                                     R 1.000                                                                             ANG                                                                              -4.077                                                                            1) -.093                                                                            2) -.517                                                                             3) 20.047                                                                            4) -.110                                     R .800                                                                              ANG                                                                              -5.500                                                                            1) -.125                                                                            2) -.472                                                                             3) 20.047                                                                            4) -.110                                     __________________________________________________________________________    Conversion Coefficient γ.sub.x Associated With Direction of Optical     Axis at Telephoto End                                                         (131.0 mm) in First Embodiment                                                __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) 1.643                                                                             3) .000                                                                              4) .000                                      R 10.000                                                                            ANG                                                                              -.315                                                                             1) .000                                                                             2) 2.051                                                                             3) .000                                                                              4) .000                                      R 5.000                                                                             ANG                                                                              -.665                                                                             1) .000                                                                             2) 2.348                                                                             3) .000                                                                              4) .000                                      R 3.000                                                                             ANG                                                                              -1.143                                                                            1) .000                                                                             2) 2.655                                                                             3) .000                                                                              4) .000                                      R 2.000                                                                             ANG                                                                              -1.784                                                                            1) .000                                                                             2) 2.954                                                                             3) .000                                                                              4) .000                                      R 1.500                                                                             ANG                                                                              -2.481                                                                            1) .000                                                                             2) 3.193                                                                             3) .000                                                                              4) .000                                      R 1.000                                                                             ANG                                                                              -4.077                                                                            1) .000                                                                             2) 3.564                                                                             3) .000                                                                              4) .000                                      R .800                                                                              ANG                                                                              -5.500                                                                            1) .000                                                                             2) 3.781                                                                             3) .000                                                                              4) .000                                      __________________________________________________________________________    Slope dx/da of Focus Cam at Telephoto End (131.0 mm) in First                 __________________________________________________________________________    Embodiment                                                                    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) -3.396                                                                            3) .000                                                                              4) .000                                      R 10.000                                                                            ANG                                                                              -.315                                                                             1) .000                                                                             2) -2.305                                                                            3) .000                                                                              4) .000                                      R 5.000                                                                             ANG                                                                              -.665                                                                             1) .000                                                                             2) -1.735                                                                            3) .000                                                                              4) .000                                      R 3.000                                                                             ANG                                                                              -1.143                                                                            1) .000                                                                             2) -1.408                                                                            3) .000                                                                              4) .000                                      R 2.000                                                                             ANG                                                                              -1.784                                                                            1) .000                                                                             2) -1.073                                                                            3) .000                                                                              4) .000                                      R 1.500                                                                             ANG                                                                              -2.481                                                                            1) .000                                                                             2) -.874                                                                             3) .000                                                                              4) .000                                      R 1.000                                                                             ANG                                                                              -4.077                                                                            1) .000                                                                             2) -.597                                                                             3) .000                                                                              4) .000                                      R .800                                                                              ANG                                                                              -5.500                                                                            1) .000                                                                             2) -.464                                                                             3) .000                                                                              4) .000                                      __________________________________________________________________________    Conversion Coefficient γ.sub.a Associated With Direction of             Rotation at Telephoto End                                                     (131.0 mm) in First Embodiment                                                __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) -5.580                                                                            3) .000                                                                              4) .000                                      R 10.000                                                                            ANG                                                                              -.315                                                                             1) .000                                                                             2) -4.727                                                                            3) .000                                                                              4) .000                                      R 5.000                                                                             ANG                                                                              -.665                                                                             1) .000                                                                             2) -4.075                                                                            3) .000                                                                              4) .000                                      R 3.000                                                                             ANG                                                                              -1.143                                                                            1) .000                                                                             2) -3.738                                                                            3) .000                                                                              4) .000                                      R 2.000                                                                             ANG                                                                              -1.784                                                                            1) .000                                                                             2) -3.169                                                                            3) .000                                                                              4) .000                                      R 1.500                                                                             ANG                                                                              -2.481                                                                            1) .000                                                                             2) -2.790                                                                            3) .000                                                                              4) .000                                      R 1.000                                                                             ANG                                                                              -4.077                                                                            1) .000                                                                             2) -2.127                                                                            3) .000                                                                              4) .000                                      R .800                                                                              ANG                                                                              -5.500                                                                            1) .000                                                                             2) -1.756                                                                            3) .000                                                                              4) .000                                      __________________________________________________________________________     Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 2.30,        γ.sub.aR /γ.sub.a0 = 0.31                                    

As can be seen from Tables 12, 13, and 14, at each focal length, theconversion coefficient γ_(x) associated with the direction of theoptical axis increases but the value of the slope (dx/da) of the focuscam decreases as the photographing distance becomes closer to theclosest distance. Therefore, as can be seen from these tables, the valueof the conversion coefficient γ_(a) associated with the direction ofrotation, which is defined as the product of the conversion coefficientγ_(x) and the slope (dx/da) of the focus cam, decreases as thephotographing distance becomes closer to the closest distance by theinfluence of the slope (dx/da) of the focus cam, contrary to theembodiment of Japanese Patent Application Laid-Open No. 5-142475.

As described above, when the ratio (Δx_(TR) /ΔX_(WR)) between theamounts Δx_(TR) and ΔX_(WR) of movement, in the direction of the opticalaxis, of the focusing lens unit required for focusing from the infinityposition to the closest distance position at the wide-angle end and thetelephoto end is large, the degree of the decrease in slope (dx/da) ofthe focus cam also becomes large. For this reason, the conversioncoefficient γ_(a) associated with the direction of rotation furtherdecreases under the influence of the slope (dx/da) of the focus cam asthe photographing distance becomes closer to the closest distance.

From Tables 12, 13, and 14, the rate of change, from the infinityin-focus position to the closest in-focus position, of the conversioncoefficient γ_(a) associated with the direction of rotation is ×0.59 atthe wide-angle end (F=36.0), ×0.50 at the middle position (F=70.0), and×0.31 at the telephoto end (F=131.0). When the number N of divisions ofthe focus range upon a change in conversion coefficient γ_(a) in thefirst embodiment is calculated using formula (a), and is compared withthat in the embodiment of Japanese Patent Application Laid-Open No.5-142475, the numbers N_(W), N_(M), and N_(T) of divisions at thewide-angle end, middle position, and telephoto end respectively have thefollowing values:

Embodiment of Japanese Patent Application Laid-Open No. 5-142475

    N.sub.W >9.3 N.sub.M >10.1 N.sub.T >8.1

First Embodiment

    N.sub.W >2.9 N.sub.M >3.8 N.sub.T >6.3

Therefore, as can be understood from a comparison with the previouslycalculated values in the embodiment of Japanese Patent ApplicationLaid-Open No. 5-142475, although the ratio (Δx_(TR) /Δx_(WR)) betweenthe amounts ΔX_(TR) and Δx_(WR) of movement, in the direction of theoptical axis, of the focusing lens unit required for focusing from theinfinity position to the closest distance position at the wide-angle endand the telephoto end in the first embodiment is larger than that in theembodiment of Japanese Patent Application Laid-Open No. 5-142475 (theembodiment of Japanese Patent Application Laid-Open No. 5-142475: 3.94;the first embodiment: 5.45), the values of the numbers N of divisionsbecome small conversely.

As described above, in the zoom lens of the first embodiment, since therate of change, from the infinity in-focus position to the closestin-focus position, of the conversion coefficient γ_(a) associated withthe direction of rotation becomes much smaller than that in theembodiment of Japanese Patent Application Laid-Open No. 5-142475, thenumber of data of the conversion coefficient γ_(a) and the correctioncoefficient μ can be reduced, and the storage capacity can besuppressed.

Tables 15, 16, and 17 summarize the calculation results of theconversion coefficient K_(a) and the correction coefficient μ at thewide-angle end (F=36.0), middle position (F=70.0), and telephoto end(F=131.0) according to the first embodiment. In these tables, (R) is theobject distance (m), (ANG) is the amount of rotation for focusing fromthe infinity corresponding position on the focus cam, (r) is theconversion coefficient γ_(a) in the direction of rotation, (rs) is theconversion coefficient K_(a), (bf) is the defocus amount (mm), and (l)is the correction coefficient μ. Each table has a matrix structure, andeight rows in the vertical direction indicated by (POS) represent theobject positions (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.80 mm), andfour pairs (R, ANGLE) in the horizontal direction represent the lensarrangements of the focusing lens unit.

More specifically, the position of the focusing lens in the first pairin the upper two tables in each of Tables 15, 16, and 17, i.e., in thethird and fourth columns is (R, ANGLE)=(0.0, 0.0), and it indicates thatthis position corresponds to the infinity corresponding position.Therefore, the third column (r) in the first table represents the valueof the conversion coefficient γ_(a) in the direction of rotation whenthe focusing lens unit is focused on an infinity object, and the fourthcolumn (rs) represents the value of the conversion coefficient K_(a)when the focusing lens unit is moved from an in-focus state on aninfinity object to an in-focus state at the object distance in thesecond column. Furthermore, the third column (bf) in the second tablerepresents the defocus amount ΔBf from a predetermined imaging positionwhen the position of the focusing lens unit corresponds to the infinitycorresponding position, and an object is located at an object distancein the second column, and the fourth column (l) represents the value ofthe correction coefficient μ when the focusing lens unit is moved froman in-focus state on an infinity object to an in-focus state at theobject distance in the second column.

Similarly, the position of the focusing lens in the fourth pair in thelower two tables in each of Tables 15, 16, and 17, i.e., in the ninthand tenth columns is (R, ANGLE)=(0.8, -5.5), and it indicates that thisposition corresponds to the closest in-focus (R=0.8 m) correspondingposition. Therefore, the ninth column (r) in the third table representsthe value of the conversion coefficient γ_(a) in the direction ofrotation when the focusing lens unit is focused on a closest distance(R=0.80 m) object, and the tenth column (rs) represents the value of theconversion coefficient K_(a) when the focusing lens unit is moved froman in-focus state on the closest distance (R=0.80 m) object to anin-focus state at the object distance in the second column. Furthermore,the ninth column (bf) in the fourth table represents the defocus amountΔBf from a predetermined imaging position when the position of thefocusing lens unit corresponds to the closest corresponding position,and the object is located at an object distance in the second column,and the tenth column (l) represents the value of the correctioncoefficient μ when the focusing lens unit is moved from an in-focusstate on the closest distance (R=0.80 m) object to an in-focus state atthe object distance in the second column.

As described above, since the conversion coefficient in the direction ofrotation is calculated by K_(a) =ΔBf/Δa (where Δa: the amount ofrotation for focusing), and the correction coefficient μ is calculatedby μ=ΔBf/(1 -K_(a) /γ_(a)), the value of the conversion coefficientK_(a) (eighth row, fourth column in first table: -0.336) when thefocusing lens unit is moved from an in-focus state on the infinityobject to an in-focus state at the object distance (R=0.80 m) in Table15 is calculated by K_(a) =1.85/-5.5=-0.336 using ΔBf=1.85 and Δa=-5.5.On the other hand, the value of the correction coefficient μ (eighthrow, fourth column in second table: 10.77) is calculated as μ=10.77using ΔBf=1.85, K_(a) =-0.336, and γ_(a)

                                      TABLE 15                                    __________________________________________________________________________    Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associated        with Direction of Rotation and                                                Correction Coefficient μ: (l) at Wide-angle End (36.0 mm) of First         Embodiment                                                                    f = 36.0 mm                                                                   __________________________________________________________________________           (R, ANGLE) =                                                                  .000                                                                             .000                                                                              10.000                                                                            -.326                                                                             5.000                                                                             -.665                                                                             3.000                                                                            -1.143                                       POS                                                                              R   r  rs  r   rs  r   rs  r  rs                                           __________________________________________________________________________    1  .000                                                                              -.406                                                                            .000    -.398   -.390  -.378                                        2  10.000 -.402                                                                             -.394                                                                             .000    -.386  -.374                                        3  5.000  -.398   -.390                                                                             -.381                                                                             .000   -.369                                        4  3.000  -.391   -.383   -.374                                                                             -.362                                                                            .000                                         5  2.000  -.382   -.374   -.365  -.354                                        6  1.500  -.373   -.365   -.357  -.346                                        7  1.000  -.353   -.345   -.337  -.327                                        8  .800   -.336   -.329   -.321  -.311                                        __________________________________________________________________________    POS                                                                              R   bf l   bf  l   bf  l   bf l                                            __________________________________________________________________________    1  .000                                                                              .00                                                                              .00 -.13                                                                              13.34                                                                             -.26                                                                              11.08                                                                             -.43                                                                             9.91                                         2  10.000                                                                            .13                                                                              14.85                                                                             .00 .00 -.13                                                                              10.30                                                                             -.31                                                                             9.62                                         3  5.000                                                                             .26                                                                              13.58                                                                             .13 11.41                                                                             .00 .00 -.18                                                                             9.62                                         4  3.000                                                                             .45                                                                              12.33                                                                             .31 10.65                                                                             .18 9.70                                                                              .00                                                                              .00                                          5  2.000                                                                             .68                                                                              11.71                                                                             .55 10.52                                                                             .41 9.98                                                                              .23                                                                              10.09                                        6  1.500                                                                             .92                                                                              11.42                                                                             .79 10.49                                                                             .65 10.07                                                                             .46                                                                              10.01                                        7  1.000                                                                             1.44                                                                             11.03                                                                             1.29                                                                              10.36                                                                             1.15                                                                              10.01                                                                             .96                                                                              9.78                                         8  .800                                                                              1.85                                                                             10.77                                                                             1.70                                                                              10.21                                                                             1.55                                                                              9.87                                                                              1.36                                                                             9.58                                         __________________________________________________________________________           (R, ANGLE) =                                                                  2.000                                                                            -1.784                                                                            1.500                                                                             -2.481                                                                            1.000                                                                             -4.077                                                                            .800                                                                             -5.500                                       POS                                                                              R   r  rs  r   rs  r   rs  r  rs                                           __________________________________________________________________________    1  .000   -.364   -.349   -.319  -.296                                        2  10.000 -.359   -.345   -.315  -.293                                        3  5.000  -.355   -.340   -.311  -.289                                        4  3.000  -.348   -.334   -.306  -.284                                        5  2.000                                                                             -.341                                                                            .000    -.327   -.298  -.277                                        6  1.500  -.332                                                                             -.319                                                                             .000    -.291  -.270                                        7  1.000  -.314   -.301                                                                             -.274                                                                             .000   -.254                                        8  .800   -.299   -.286   -.261                                                                             -.241                                                                            .000                                         __________________________________________________________________________    POS                                                                              R   bf l   bf  l   bf  l   bf l                                            __________________________________________________________________________    1  .000                                                                              -.65                                                                             9.60                                                                              -.87                                                                              9.13                                                                              -1.30                                                                             8.00                                                                              -1.63                                                                            7.13                                         2  10.000                                                                            -.52                                                                             9.52                                                                              -.74                                                                              9.08                                                                              -1.18                                                                             7.96                                                                              -1.51                                                                            7.09                                         3  5.000                                                                             -.40                                                                             9.57                                                                              -.62                                                                              9.09                                                                              -1.06                                                                             7.93                                                                              -1.40                                                                            7.07                                         4  3.000                                                                             -.22                                                                             9.62                                                                              -.45                                                                              9.08                                                                              -.90                                                                              7.89                                                                              -1.24                                                                            7.02                                         5  2.000                                                                             .00                                                                              .00 -.23                                                                              9.00                                                                              -.68                                                                              7.81                                                                              -1.03                                                                            6.96                                         6  1.500                                                                             .23                                                                              9.48                                                                              .00 .00 -.46                                                                              7.74                                                                              -.81                                                                             6.89                                         7  1.000                                                                             .72                                                                              9.23                                                                              .48 8.65                                                                              .00 .00 -.36                                                                             6.78                                         8  .800                                                                              1.11                                                                             9.04                                                                              .86 8.47                                                                              .37 7.34                                                                              .00                                                                              .00                                          __________________________________________________________________________     Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.83, K.sub.aR     /γ.sub.aR = 1.23                                                   

                                      TABLE 16                                    __________________________________________________________________________    Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associated        with Direction of Rotation and                                                Correction Coefficient μ: (l) at Middle Position (70.0 mm) of First        Embodiment                                                                    f = 70.0 mm                                                                   __________________________________________________________________________           (R, ANGLE) =                                                                  .000                                                                              .000                                                                              10.000                                                                            -.326                                                                             5.000                                                                             -.666                                                                             3.000                                                                             -1.143                                     POS                                                                              R   r   rs  r   rs  r   rs  r   rs                                         __________________________________________________________________________    1  .000                                                                              -1.537                                                                            .000    -1.476  -1.419  -1.347                                     2  10.000  -1.522                                                                            -1.463                                                                            .000    -1.407  -1.335                                     3  5.000   -1.509  -1.450                                                                            -1.394                                                                            .000    -1.323                                     4  3.000   -1.490  -1.432  -1.376                                                                            -1.305                                                                            .000                                       5  2.000   -1.465  -1.407  -1.352  -1.282                                        1.500   -1.439  -1.381  -1.327  -1.258                                     7  1.000   -1.375  -1.319  -1.266  -1.199                                     8  .800    -1.316  -1.262  -1.210  -1.144                                     __________________________________________________________________________    POS                                                                              R   bf  l   bf  l   bf  l   bf  l                                          __________________________________________________________________________    1  .000                                                                              .00 .00 -.48                                                                              53.19                                                                             -.95                                                                              51.96                                                                             -1.54                                                                             47.64                                      2  10.000                                                                            .50 52.50                                                                             .00 .00 -.48                                                                              51.66                                                                             -1.09                                                                             47.24                                      3  5.000                                                                             1.00                                                                              55.06                                                                             .49 55.84                                                                             .00 .00 -.63                                                                              46.69                                      4  3.000                                                                             1.70                                                                              55.79                                                                             1.17                                                                              54.69                                                                             .66 50.96                                                                             .00 .00                                        5  2.000                                                                             2.61                                                                              55.63                                                                             2.05                                                                              53.61                                                                             1.51                                                                              50.01                                                                             .82 46.00                                      6  1.500                                                                             3.56                                                                              55.60                                                                             2.97                                                                              53.32                                                                             2.40                                                                              50.07                                                                             1.67                                                                              46.69                                      7  1.000                                                                             5.59                                                                              53.03                                                                             4.93                                                                              50.24                                                                             4.30                                                                              46.95                                                                             3.50                                                                              43.01                                      8  .800                                                                              7.24                                                                              50.33                                                                             6.53                                                                              47.43                                                                             5.85                                                                              44.25                                                                             4.98                                                                              40.37                                      __________________________________________________________________________           (R, ANGLE) =                                                                  2.000                                                                             -1.782                                                                            1.500                                                                             -2.474                                                                            1.000                                                                             -4.063                                                                            .800                                                                              -5.500                                     POS                                                                              R   r   rs  r   rs  r   rs  r   rs                                         __________________________________________________________________________    1  .000    -1.263  -1.183  -1.033  -.926                                      2  10.000  -1.251  -1.172  -1.023  -.916                                      3  5.000   -1.239  -1.161  -1.012  -.906                                      4  3.000   -1.222  -1.145  -.997   -.891                                      5  2.000                                                                             -1.200                                                                            .000    -1.125  -.977   -.872                                      6  1.500   -1.178                                                                            -1.101                                                                            .000    -.954   -.850                                      7  1.000   -1.120  -1.044                                                                            -.900                                                                             .000    -.801                                      8  .800    -1.067  -.993   -.855                                                                             -.762                                                                             .000                                       __________________________________________________________________________    POS                                                                              R   bf  l   bf  l   bf  l   bf  l                                          __________________________________________________________________________    1  .000                                                                              -2.25                                                                             43.31                                                                             -2.93                                                                             39.16                                                                             -4.20                                                                             28.27                                                                             -5.09                                                                             23.74                                      2  10.000                                                                            -1.82                                                                             43.08                                                                             -2.52                                                                             38.91                                                                             -3.82                                                                             27.91                                                                             -4.74                                                                             23.52                                      3  5.000                                                                             -1.38                                                                             42.89                                                                             -2.10                                                                             38.63                                                                             -3.44                                                                             27.50                                                                             -4.38                                                                             23.29                                      4  3.000                                                                             -.78                                                                              42.92                                                                             -1.52                                                                             38.15                                                                             -2.91                                                                             26.89                                                                             -3.88                                                                             22.97                                      5  2.000                                                                             .00 .00 -.78                                                                              36.13                                                                             -2.23                                                                             25.92                                                                             -3.24                                                                             22.55                                      6  1.500                                                                             .81 44.67                                                                             .00 .00 -1.52                                                                             25.00                                                                             -2.57                                                                             22.29                                      7  1.000                                                                             2.55                                                                              38.09                                                                             1.66                                                                              31.93                                                                             .00 .00 -1.15                                                                             22.72                                      8  .800                                                                              3.97                                                                              35.61                                                                             3.00                                                                              30.54                                                                             1.23                                                                              24.56                                                                             .00 .00                                        __________________________________________________________________________     Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.86, K.sub.aR     /γ.sub.aR = 1.21                                                   

                                      TABLE 17                                    __________________________________________________________________________    Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associated        with Direction of Rotation and Correction                                     Coefficient μ: (l) at Telephoto End (131.0 mm) of First Embodiment         f = 131.0 mm                                                                  __________________________________________________________________________           (R, ANGLE) =                                                                  .000                                                                              .000                                                                              10.000                                                                            -.315                                                                             5.000                                                                             -.665                                                                              3.000                                                                             -1.143                                    POS                                                                              R   r   rs  r   rs  r   rs   r   rs                                        __________________________________________________________________________    1  .000                                                                              -5.581                                                                            .000    -4.865  -4.233   -3.743                                    2  10.000  -5.566                                                                            -4.728                                                                            .000    -4.102   -3.684                                    3  5.000   -5.399  -4.571                                                                            -4.076                                                                            .000     -3.714                                    4  3.000   -5.400  -4.637  -4.194                                                                             -3.738                                                                            .000                                      5  2.000   -5.401  -4.646  -4.170   -3.663                                    6  1.500   -5.401  -4.639  -4.144   -3.632                                    7  1.000   -5.393  -4.603  -4.081   -3.557                                    8  .800    -5.374  -4.557  -4.017   -3.485                                    __________________________________________________________________________    POS                                                                              R   bf  l   bf  l   bf  l    bf  l                                         __________________________________________________________________________    1  .000                                                                              .00 .00 -1.53                                                                             52.72                                                                             -2.81                                                                             73.26                                                                              -4.28                                                                             3639.88                                   2  10.000                                                                            1.75                                                                              650.22                                                                            .00 .00 -1.43                                                                             221.92                                                                             -3.05                                                                             -210.62                                   3  5.000                                                                             3.59                                                                              109.65                                                                            1.60                                                                              48.25                                                                             .00 .00  -1.77                                                                             -273.24                                   4  3.000                                                                             6.17                                                                              190.29                                                                            3.84                                                                              201.20                                                                            2.00                                                                              -69.39                                                                             .00 .00                                       5  2.000                                                                             9.64                                                                              297.66                                                                            6.83                                                                              396.74                                                                            4.67                                                                              -203.05                                                                            2.35                                                                              116.66                                    6  1.500                                                                             13.40                                                                             413.92                                                                            10.05                                                                             539.04                                                                            7.53                                                                              -448.77                                                                            4.86                                                                              171.61                                    7  1.000                                                                             21.98                                                                             649.65                                                                            17.31                                                                             656.86                                                                            13.92                                                                             -11862.3                                                                           10.44                                                                             215.51                                    8  .800                                                                              29.56                                                                             794.07                                                                            23.63                                                                             653.40                                                                            19.42                                                                             1341.29                                                                            15.19                                                                             224.15                                    __________________________________________________________________________           (R, ANGLE) =                                                                  2.000                                                                             -1.784                                                                            1.500                                                                             -2.481                                                                            1.000                                                                             -4.077                                                                             .800                                                                              -5.500                                    POS                                                                              R   r   rs  r   rs  r   rs   r   rs                                        __________________________________________________________________________    1  .000    -3.275  -2.905  -2.338   -2.006                                    2  10.000  -3.237  -2.875  -2.316   -1.986                                    3  5.000   -3.242  -2.871  -2.305   -1.974                                    4  3.000   -3.218  -2.847  -2.281   -1.951                                    5  2.000                                                                             -3.170                                                                            .000    -2.815  -2.250   -1.921                                    6  1.500   -3.153                                                                            -2.789                                                                            .000    -2.215   -1.888                                    7  1.000   -3.072  -2.697                                                                            -2.126                                                                            .000     -1.814                                    8  .800    -2.996  -2.622  -2.065                                                                             -1.755                                                                            .000                                      __________________________________________________________________________    POS                                                                              R   bf  l   bf  l   bf  l    bf  l                                         __________________________________________________________________________    1  .000                                                                              -5.84                                                                             177.43                                                                            -7.21                                                                             173.40                                                                            -9.53                                                                             95.33                                                                              -11.03                                                                            77.30                                     2  10.000                                                                            -4.76                                                                             226.43                                                                            -6.23                                                                             201.39                                                                            -8.71                                                                             97.38                                                                              -10.30                                                                            78.22                                     3  5.000                                                                             -3.63                                                                             160.30                                                                            -5.21                                                                             176.99                                                                            -7.86                                                                             93.25                                                                              -9.54                                                                             76.61                                     4  3.000                                                                             -2.06                                                                             136.87                                                                            -3.81                                                                             183.66                                                                            -6.69                                                                             91.50                                                                              -8.50                                                                             76.16                                     5  2.000                                                                             .00 .00 -1.96                                                                             209.91                                                                            -5.16                                                                             88.44                                                                              -7.14                                                                             75.56                                     6  1.500                                                                             2.20                                                                              417.74                                                                            .00 .00 -3.53                                                                             83.95                                                                              -5.70                                                                             75.19                                     7  1.000                                                                             7.04                                                                              227.93                                                                            4.30                                                                              130.79                                                                            .00 .00  -2.58                                                                             77.62                                     8  .800                                                                              11.13                                                                             203.25                                                                            7.91                                                                              131.93                                                                            2.94                                                                              102.84                                                                             .00 .00                                       __________________________________________________________________________     Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.96, K.sub.aR     /γ.sub.aR = 1.14                                                   

As can be seen from Tables 15, 16, and 17 above, when a change inconversion coefficient K_(a) : (rs) (e.g., the fourth column in thefirst table) at a given lens arrangement (e.g., at the infinity in-focusarrangement) is considered, the rate of change becomes small as comparedto the change in K_(a) (Tables 6, 7, and 8) in the embodiment ofJapanese Patent Application Laid-Open No. 5-142475 examined previously.

More specifically, the amount Aa of rotation for focusing in the firstembodiment at the infinity object side becomes relatively smaller thanthat at the closest object side, as compared to Japanese PatentApplication Laid-Open No. 5-142475. In fact, when the ratio between theamount of rotation for focusing upon focusing to the closest distanceand the amount of rotation for focusing upon focusing to the objectdistance (R=5.0 m) is calculated in Tables 1 and 10, 3.379/10.0=0.338 inthe embodiment of Japanese Patent Application Laid-Open No. 5-142475,while -0.665/-5.5=0.121 in the first embodiment. As described above,when the focus cam with the arrangement of the present invention isused, since the amount Δa of rotation for focusing becomes relativelysmaller at the infinity object side, the conversion coefficient K_(a)becomes relatively large at the infinity object side, and consequently,the change in conversion coefficient K_(a) in the direction of rotationcan be reduced as compared to the conventional system.

The calculation results of the rate of change of K_(a) with respect toγ_(a) at the infinity in-focus arrangement and the closest in-focusarrangement at the wide-angle end, middle position, and telephoto end inthe embodiment of Japanese Patent Application Laid-Open No. 5-142475 andin the first embodiment of the present invention are as follows.

    ______________________________________                                        Embodiment of Japanese Patent Application Laid-Open No. 5-142475                       Infinity Arrangement                                                                       Closest Arrangement                                              K.sub.aO /γ.sub.aO                                                                   K.sub.aR /γ.sub.aR                                ______________________________________                                        Wide-angle End                                                                           2.75           0.44                                                (F = 36.0)                                                                    Middle Position                                                                          3.36           0.43                                                (F = 50.0)                                                                    Telephoto End                                                                            3.80           0.43                                                (F = 103.0)                                                                   First Embodiment                                                              Wide-angle End                                                                           0.83           1.23                                                (F = 36.0)                                                                    Middle Position                                                                          0.86           1.21                                                (F = 70.0)                                                                    Telephoto End                                                                            0.96           1.14                                                (F = 131.0)                                                                   ______________________________________                                    

As described above, according to the present invention, since the rateof change of K_(a) with respect to γ_(a) is small as compared to theconventional system, and the contribution of the correction term (ΔBf/μ)in K_(a) =γ_(a) (1-ΔBf/μ) can be reduced, the value of the correctioncoefficient p can be set to be large as compared to the defocus amountΔBf, and at the same time, the change in correction coefficient μ can bedecreased.

Therefore, even when only a pair of a conversion coefficient γ_(a) valueand a correction coefficient μ value are set for a given lensarrangement range, an error in the conversion coefficient K_(a)calculated using γ_(a) and μ or in the actual lens driving amount Δ_(a)for focusing can be eliminated.

Next, in the embodiment of Japanese Patent Application Laid-Open No.5-142475 and the first embodiment of the present invention, when thelens driving amounts upon focusing from the infinity in-focus lensarrangement to the closest distance object and upon focusing from theclosest in-focus lens arrangement to the infinity object at thewide-angle end, middle position, and telephoto end are calculated fromΔa=ΔBf/ γ_(a) (1-ΔBf/μ)!, and errors from the actual lens drivingamounts are then calculated, the following values are obtained. Notethat the value of the correction coefficient μ upon focusing from theinfinity in-focus lens arrangement to the closest distance object adoptsa value at the object distance (POS-6), and the value of the correctioncoefficient μ upon focusing from the closest in-focus lens arrangementto the infinity object adopts a value at the object distance (POS-4).

    ______________________________________                                        Embodiment of Japanese Patent Application Laid-Open No. 5-142475                      Infinity Arrangement →                                                              Closest Arrangement →                                     Closest In-focus State                                                                     Infinity In-focus State                                  ______________________________________                                        Wide-angle End                                                                          -4.4%          -13.0%                                               (F = 36.0)                                                                    Middle Position                                                                         -8.2%          -12.0%                                               (F = 50.0)                                                                    Telephoto End                                                                           -8.8%          -14.6%                                               (F = 103.0)                                                                   First Embodiment                                                              Wide-angle End                                                                          -1.1%          -0.2%                                                (F = 36.0)                                                                    Middle Position                                                                         -1.5%          -0.6%                                                (F = 70.0)                                                                    Telephoto End                                                                           3.7%           -0.2%                                                (F = 131.0)                                                                   ______________________________________                                    

As described above, even when only a pair of a conversion coefficientγ_(a) value and a correction coefficient μ value are set for a givenlens arrangement range, an error between the conversion coefficientK_(a) calculated from γ_(a) and μ and the lens driving amount Δa forfocusing becomes small as compared to the conventional system, andfocusing can be realized with higher accuracy.

For the sake of reference, when errors of the lens driving amounts uponfocusing from the infinity in-focus lens arrangement to the objectdistance (R=10.0 m) and upon focusing from the closest in-focus lensarrangement to the object distance (R=1.0 m) are calculated andcompared, the following results are obtained. As can be seen from thesetables, focusing accuracy can be relatively improved independently ofthe object distance.

    ______________________________________                                        Embodiment of Japanese Patent Application Laid-Open No. 5-142475                      Infinity Arrangement →                                                              Closest Arrangement →                                     10-m In-focus State                                                                        1-m In-focus State                                       ______________________________________                                        Wide-angle End                                                                          -6.7%          1.5%                                                 (F = 36.0)                                                                    Middle Position                                                                         4.1%           2.5%                                                 (F = 50.0)                                                                    Telephoto End                                                                           6.2%           2.4%                                                 (F = 103.0)                                                                   First Embodiment                                                              Wide-angle End                                                                          -0.6%          -0.1%                                                (F = 36.0)                                                                    Middle Position                                                                         0.7%           0.0%                                                 (F = 70.0)                                                                    Telephoto End                                                                           -0.0%          -0.1%                                                (F = 131.0)                                                                   ______________________________________                                    

Next, an examination will be made as to whether not only accurateauto-focusing but also so-called manual focusing can be attained in thezoom lens of the first embodiment.

Table 18 summarizes the amount (ANGLE DA) of rotation for focusing uponmanual focusing using the focus cam (the middle table in Table 10) ofthe first embodiment, the amount DX (mm) of movement, in the directionof the optical axis, of the focusing lens unit corresponding to theamount of rotation for focusing, and the displacement amount Bf (mm) ofthe imaging point when the amount (DX) of movement in the direction ofthe optical axis is given.

The upper table in Table 18 summarizes the displacement amount (Bf) ofthe imaging point corresponding to the photographing distances (R=5.0,3.0, 2.0, 1.5, 1.0, and 0.80 m) in the respective zooming states of thefocal lengths (F=36.0, 50.0, 70.0, 85.0, 105.0, and 131.0 mm), and themiddle table summarizes the values of the amount (ANGLE DA) of rotationfor focusing required for attaining an optimal in-focus state withrespect to the respective photographing distances (R=5.0, 3.0, 2.0, 1.5,1.0, and 0.80 m). Note that the amounts of rotation for focusing, whichhave values for eliminating any displacement of the imaging point at thewide-angle end and the telephoto end, are selected. The lower tablesummarizes the amounts (DX) of movement, in the direction of the opticalaxis, of the respective lens units corresponding to the amount (ANGLEDA) of rotation for focusing in association with the photographingdistances (R=5.0, 3.0, 2.0, 1.5, 1.0, and 0.80 m) in the respectivezooming states with the focal lengths (F=36.0, 50.0, 70.0, 85.0, 105.0,and 131.0 mm). In the lower table, (F) is the focal length (mm) of theentire system, (R) is the photographing distance (m), and (DX) is theamount (mm) of movement, in the direction of the optical axis, of eachof the first, second, third, and fourth lens units in turn from theright side. Note that the amount of movement in the direction of theoptical axis toward the object side is represented by a positive value.

                  TABLE 18                                                        ______________________________________                                        Displacement Amount Bf (mm) of Imaging Point and Amount DX                    (mm) of movement for focusing in First Embodiment                                      0.80 m  1.00 m  1.50 m                                                                              2.00 m                                                                              3.00 m                                                                              5.00 m                             ______________________________________                                         36.000 Bf                                                                             .000    .000    .000  .000  .000  .000                                50.000 Bf                                                                             .000    .003    .002  -.002 -.004 -.004                               70.000 Bf                                                                             .000    -.012   -.008 -.003 .000  .001                                85.000 Bf                                                                             .000    .002    .006  .002  -.004 -.003                              105.000 Bf                                                                             .000    .010    -.001 .000  .004  -.005                              131.000 Bf                                                                             .000    .000    .000  .000  .000  .000                               ANGLE DA -5.500  -4.077  -2.481                                                                              -1.784                                                                              -1.143                                                                              -.665                              ______________________________________                                        F   36.000 DX  .000    1.041 .000  .000 R 0.80 m                              F   50.000 DX  .000    1.500 .000  .000 R 0.80 m                              F   70.000 DX  .000    2.296 .000  .000 R 0.80 m                              F   85.000 DX  .000    2.994 .000  .000 R 0.80 m                              F   105.000 DX .000    4.063 .000  .000 R 0.80 m                              F   131.000 DX .000    5.676 .000  .000 R 0.80 m                              F   36.000 DX  .000    .825  .000  .000 R 1.00 m                              F   50.000 DX  .000    1.198 .000  .000 R 1.00 m                              F   70.000 DX  .000    1.872 .000  .000 R 1.00 m                              F   85.000 DX  .000    2.470 .000  .000 R 1.00 m                              F   105.000 DX .000    3.423 .000  .000 R 1.00 m                              F   131.000 DX .000    4.928 .000  .000 R 1.00 m                              F   36.000 DX  .000    .544  .000  .000 R 1.50 m                              F   50.000 DX  .000    .800  .000  .000 R 1.50 m                              F   70.000 DX  .000    1.281 .000  .000 R 1.50 m                              F   85.000 DX  .000    1.728 .000  .000 R 1.50 m                              F   105.000 DX .000    2.488 .000  .000 R 1.50 m                              F   131.000 DX .000    3.780 .000  .000 R 1.50 m                              F   36.000 DX  .000    .405  .000  .000 R 2.00 m                              F   50.000 DX  .000    .602  .000  .000 R 2.00 m                              F   70.000 DX  .000    .974  .000  .000 R 2.00 m                              F   85.000 DX  .000    1.334 .000  .000 R 2.00 m                              F   105.000 DX .000    1.965 .000  .000 R 2.00 m                              F   131.000 DX .000    3.106 .000  .000 R 2.00 m                              F   36.000 DX  .000    .269  .000  .000 R 3.00 m                              F   50.000 DX  .000    .403  .000  .000 R 3.00 m                              F   70.000 DX  .000    .659  .000  .000 R 3.00 m                              F   85.000 DX  .000    .920  .000  .000 R 3.00 m                              F   105.000 DX .000    1.391 .000  .000 R 3.00 m                              F   131.000 DX .000    2.323 .000  .000 R 3.00 m                              F   36.000 DX  .000    .161  .000  .000 R 5.00 m                              F   50.000 DX  .000    .243  .000  .000 R 5.00 m                              F   70.000 DX  .000    .400  .000  .000 R 5.00 m                              F   85.000 DX  .000    .568  .000  .000 R 5.00 m                              F   105.000 DX .000    .886  .000  .000 R 5.00 m                              F   131.000 DX .000    1.571 .000  .000 R 5.00 m                              ______________________________________                                    

As can be seen from Table 18, so-called manual focusing can be attainedsince the displacement amounts of the imaging point at the respectivefocal lengths and photographing distances are very small, and fallwithin the depth of focus independently of the zooming state andphotographing distance.

Second Embodiment!

The second embodiment is directed to a zoom lens which has a four-unitarrangement, i.e., positive, negative, positive, and positive lensunits, and attains focusing by a negative second lens unit. In this zoomlens, the rotation amount ratio (a_(F) /a_(Z)) of the rotation amountfor focusing from the infinity in-focus position to the closest in-focusposition (R=0.5 m) to the amount of rotation for zooming from thewide-angle end (F=28.8) to the telephoto end (F=103.0) is set to be-0.60.

Table 19 below summarizes various paraxial data of an optical system anddata for defining the shape of a focus cam according to the secondembodiment.

The upper table in Table 19 summarizes the focal lengths and principalpoint interval data of the respective lens units of the optical systemcorresponding to the second embodiment in association with six zoomingstates (focal length F=28.8 (1-POS), 35.0 (2-POS), 50.0 (3-POS), 70.0(4-POS), 85.0 (5-POS) and 103.0 mm (6-POS)).

The middle table in Table 19 summarizes spline sample data when theshape of the focus cam in the second lens unit of the second embodiment,which is used for focusing, is expressed by a spline function associatedwith the angle a of rotation of a rotatable lens barrel and the amount xof movement in the direction of the optical axis. In this middle table,(1), (2), (3), and (4) correspond to the first, second, third, andfourth lens units, respectively.

Furthermore, the lower table in Table 19 summarizes the infinityfocusing positions (infinity corresponding positions) at the respectivefocal lengths (F=28.8, 35.0, 50.0, 70.0, 85.0, and 103.0 mm), and theamounts of rotation (amounts of rotation for focusing) upon focusing torespective photographing distances (R=5.0, 3.0, 2.0, 1.0, 0.7, and 0.5m) using the focus cam of the second embodiment. In this table, sincethe amount of rotation for zooming from the wide-angle end (F=28.8) tothe telephoto end (F=103.0) is set to be 10.0, and the amount ofrotation for focusing from the infinity in-focus position to the closestin-focus position (R=0.5 m) is set to be -0.60, the rotation amountratio (a_(F) /a_(Z)) of the amount of rotation for focusing to theamount of rotation for zooming in the second embodiment is

                                      TABLE 19                                    __________________________________________________________________________    Second Embodiment f = 28.8 to 103.0 (Rotation Amount Ratio:                   a.sub.p /a.sub.z = -0.6)                                                      __________________________________________________________________________    Focal lengths and Principal Point Intervals of Lens Units of Second           Embodiment                                                                               1-POS                                                                             2-POS                                                                             3-POS                                                                              4-POS                                                                             5-POS                                                                             6-POS                                                 F  28.8000                                                                           35.0000                                                                           50.0000                                                                            70.0000                                                                           85.0000                                                                           103.0000                                      __________________________________________________________________________    F1 70.5000                                                                            D1  9.3252                                                                           13.0113                                                                           20.5346                                                                            28.4581                                                                           32.6851                                                                           36.5544                                       F2 -13.4000                                                                           D2 18.3082                                                                           16.1329                                                                           13.0216                                                                            10.6580                                                                           9.2279                                                                            7.6539                                        F3 32.9000                                                                            D3 14.6453                                                                           13.3678                                                                           10.4573                                                                             8.4188                                                                           7.8210                                                                            7.5173                                        F4 56.4000                                                                            D4 49.9916                                                                           54.4242                                                                           61.6013                                                                            65.7605                                                                           67.3873                                                                           68.3296                                       __________________________________________________________________________    Focus Cam Shape (Spline Interpolation Sample Point) Corresponding             to Second Embodiment                                                            ANGLE      (1)                                                                              (2)      (3)                                                                              (4)                                               __________________________________________________________________________    1 -10.0000   .0000                                                                            1.3300   .0000                                                                            .0000                                             2 -6.0000    .0000                                                                            .9281    .0000                                                                            .0000                                             3 -3.7613    .0000                                                                            .6450    .0000                                                                            .0000                                             4 -2.4156    .0000                                                                            .4427    .0000                                                                            .0000                                             5 -1.1038    .0000                                                                            .2166    .0000                                                                            .0000                                             6 -.7153     .0000                                                                            .1434    .0000                                                                            .0000                                             7 -.4198     .0000                                                                            .0856    .0000                                                                            .0000                                             8 .0000      .0000                                                                            .0000    .0000                                                                            .0000                                             9 4.0000     .0000                                                                            -1.0616  .0000                                                                            .0000                                             10                                                                              6.2387     .0000                                                                            -2.0040  .0000                                                                            .0000                                             11                                                                              7.5844     .0000                                                                            -2.8073  .0000                                                                            .0000                                             12                                                                              8.8962     .0000                                                                            -3.9220  .0000                                                                            .0000                                             13                                                                              9.2847     .0000                                                                            -4.3611  .0000                                                                            .0000                                             14                                                                              9.5802     .0000                                                                            -4.7492  .0000                                                                            .0000                                             15                                                                              10.0000    .0000                                                                            -5.4178  .0000                                                                            .0000                                             16                                                                              11.0000    .0000                                                                            -7.7000  .0000                                                                            .0000                                             __________________________________________________________________________    Amount of Rotation for Zooming and Amount of Rotation for Focusing of         Second Embodiment                                                             (Rotation Amount Ratio: a.sub.p /a.sub.z = -0.6)                                    Infinity           Amount of                                                  Correspond-  Photograph-                                                                         Rotation for                                         Focal Length                                                                        ing Position ing Distance                                                                        Focusing                                             __________________________________________________________________________    28.8 mm                                                                             .0000        5.00 m                                                                              -.420                                                35.0 mm                                                                             1.5406       3.00 m                                                                              -.715                                                50.0 mm                                                                             4.6134       2.00 m                                                                              -1.104                                               70.0 mm                                                                             7.5428       1.00 m                                                                              -2.416                                               85.0 mm                                                                             8.9225       0.70 m                                                                              -3.761                                               103.0 mm                                                                            10.0000      0.50 m                                                                              -6.000                                               __________________________________________________________________________    Condition Corresponding Value (1)                                                                  1.55                                                     Condition Corresponding Value (2)                                                                  4.69                                                     Condition Corresponding Value (3)                                                                  -0.60                                                    Condition Corresponding Value (4)                                                                  0.57 (wide-angle end)                                                         0.29 (telephoto end)                                     Condition Corresponding Value (5)                                                                  0.81 (wide-angle end)                                                         0.98 (telephoto end)                                     Condition Corresponding Value (6)                                                                  1.25 (wide-angle end)                                                         1.19 (telephoto end)                                     __________________________________________________________________________

Table 20 below summarizes the numerical value data of the cams of thefocusing lens unit in the second embodiment, which data are calculatedby interpolation based on a spline function on the basis of the sampledata of the focus cam summarized in the middle table in Table 19. Notethat the meanings of the reference symbols in Table 20 are the same asthose in the first embodiment.

                  TABLE 20                                                        ______________________________________                                        Cam Numerical Value Data of                                                   Focusing Lens Unit in Second Embodiment                                       Focus Cam        Zoom Compensation Cam                                        Numerical Value Data                                                                           Numerical Value Data                                         ANGLE (2)      F         ANGLE  (2)    F                                      ______________________________________                                        -6.0000                                                                             .9281    .0000                                                          -5.5000                                                                             .8699    .0000                                                          -5.0000                                                                             .8090    .0000                                                          -4.5000                                                                             .7451    .0000                                                          -4.0000                                                                             .6781    .0000                                                          -3.5000                                                                             .6078    .0000                                                          -3.0000                                                                             .5340    .0000                                                          -2.5000                                                                             .4563    .0000                                                          -2.0000                                                                             .3744    .0000                                                          -1.5000                                                                             .2882    .0000                                                          -1.0000                                                                             .1974    .0000                                                          -.5000                                                                              .1015    .0000                                                          .0000 .0000    28.8000   .0000  .0000  28.8000                                .5000 -.1063   30.7391   .5000  .4390  30.7391                                1.0000                                                                              -.2181   32.7416   1.0000 .8703  32.7416                                1.5000                                                                              -.3363   34.8265   1.5000 1.2923 34.8265                                2.0000                                                                              -.4621   37.0080   2.0000 1.7022 37.0080                                2.5000                                                                              -.5964   39.2914   2.5000 2.0943 39.2914                                3.0000                                                                              -.7404   41.6760   3.0000 2.4616 41.6760                                3.5000                                                                              -.8951   44.1562   3.5000 2.7983 44.1562                                4.0000                                                                              -1.0616  46.7250   4.0000 3.0999 46.7250                                4.5000                                                                              -1.2412  49.3823   4.5000 3.3643 49.3823                                5.0000                                                                              -1.4364  52.1572   5.0000 3.5933 52.1572                                5.5000                                                                              -1.6497  55.0961   5.5000 3.7980 55.0961                                6.0000                                                                              -1.8840  58.2406   6.0000 3.9922 58.2406                                6.5000                                                                              -2.1419  61.6574   6.5000 4.1888 61.6574                                7.0000                                                                              -2.4281  65.4192   7.0000 4.4018 65.4192                                7.5000                                                                              -2.7492  69.6177   7.5000 4.6476 69.6177                                8.0000                                                                              -3.1128  74.3483   8.0000 4.9354 74.3483                                8.5000                                                                              -3.5344  79.7698   8.5000 5.2266 79.7698                                9.0000                                                                              -4.0328  86.0321   9.0000 5.4755 86.0321                                9.5000                                                                              -4.6386  93.4780   9.5000 5.6917 93.4780                                10.0000                                                                             -5.4178  103.0000  10.0000                                                                              5.9735 103.0000                               ______________________________________                                    

The left table in Table 20 summarizes the numerical value data of thefocus cam of the second embodiment, and the right table in Table 20summarizes the numerical value data of the zoom compensation cam of thisembodiment. A value obtained by synthesizing the amounts (2) of movementin the direction of the optical axis in the numerical value data of thefocus cam and the zoom compensation cam in the range from the amount ofrotation (ANGLE=0.0) to the amount of rotation (ANGLE=10.0) coincideswith the movement locus of the second lens unit calculated using theparaxial data in the upper table in Table 19.

Tables 21, 22, and 23 below summarize the amount DX (mm) of movement forfocusing, in the direction of the optical axis, of the focusing lensunit, the imaging magnifications β_(k) of the respective lens units, theconversion coefficient γ_(x) associated with the direction of theoptical axis, the slope (dx/da) of the focus cam, and the conversioncoefficient γ_(a) associated with the direction of rotation at thewide-angle end (F=28.8), the middle position (F=50.0), and the telephotoend (F=103.0) according to the second embodiment, respectively. Thearrangements of the respective tables and the meanings of the referencesymbols are the same as those in the first embodiment.

                                      TABLE 21                                    __________________________________________________________________________    Amount DX (mm) of Movement for Focusing in Direction of Optical Axis at       Wide-angle                                                                    End (28.8 mm) in Second Embodiment                                            __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) .000                                                                             3) .000                                                                              4) .000                                       R 10.000                                                                            ANG                                                                              -.207                                                                             1) .000                                                                             2) .043                                                                             3) .000                                                                              4) .000                                       R 5.000                                                                             ANG                                                                              -.420                                                                             1) .000                                                                             2) .086                                                                             3) .000                                                                              4) .000                                       R 3.000                                                                             ANG                                                                              -.715                                                                             1) .000                                                                             2) .143                                                                             3) .000                                                                              4) .000                                       R 2.000                                                                             ANG                                                                              -1.104                                                                            1) .000                                                                             2) .217                                                                             3) .000                                                                              4) .000                                       R 1.000                                                                             ANG                                                                              -2.416                                                                            1) .000                                                                             2) .443                                                                             3) .000                                                                              4) .000                                       R .700                                                                              ANG                                                                              -3.761                                                                            1) .000                                                                             2) .645                                                                             3) .000                                                                              4) .000                                       R .500                                                                              ANG                                                                              -6.000                                                                            1) .000                                                                             2) .928                                                                             3) .000                                                                              4) .000                                       __________________________________________________________________________    Imaging Magnification β.sub.K of Lens Units at Wide-angle End (28.8      mm) in Second                                                                 Embodiment                                                                    __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) -.280                                                                            3) -12.818                                                                           4) .114                                       R 10.000                                                                            ANG                                                                              -.207                                                                             1) -.007                                                                            2) -.277                                                                            3) -12.818                                                                           4) .114                                       R 5.000                                                                             ANG                                                                              -.420                                                                             1) -.015                                                                            2) -.274                                                                            3) -12.818                                                                           4) .114                                       R 3.000                                                                             ANG                                                                              -.715                                                                             1) -.025                                                                            2) -.270                                                                            3) -12.818                                                                           4) .114                                       R 2.000                                                                             ANG                                                                              -1.104                                                                            1) -.038                                                                            2) -.264                                                                            3) -12.818                                                                           4) .114                                       R 1.000                                                                             ANG                                                                              -2.416                                                                            1) -.084                                                                            2) -.247                                                                            3) -12.818                                                                           4) .114                                       R .700                                                                              ANG                                                                              -3.761                                                                            1) -.131                                                                            2) -.232                                                                            3) -12.818                                                                           4) .114                                       R .500                                                                              ANG                                                                              -6.000                                                                            1) -.209                                                                            2) -.211                                                                            3) -12.818                                                                           4) .114                                       __________________________________________________________________________    Conversion Coefficient γ.sub.x Associated With Direction of Optical     Axis at Wide-angle End                                                        (28.8 mm) in Second Embodiment                                                __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) 1.954                                                                            3) .000                                                                              4) .000                                       R 10.000                                                                            ANG                                                                              -.207                                                                             1) .000                                                                             2) 1.958                                                                            3) .000                                                                              4) .000                                       R 5.000                                                                             ANG                                                                              -.420                                                                             1) .000                                                                             2) 1.962                                                                            3) .000                                                                              4) .000                                       R 3.000                                                                             ANG                                                                              -.715                                                                             1) .000                                                                             2) 1.967                                                                            3) .000                                                                              4) .000                                       R 2.000                                                                             ANG                                                                              -1.104                                                                            1) .000                                                                             2) 1.973                                                                            3) .000                                                                              4) .000                                       R 1.000                                                                             ANG                                                                              -2.416                                                                            1) .000                                                                             2) 1.991                                                                            3) .000                                                                              4) .000                                       R .700                                                                              ANG                                                                              -3.761                                                                            1) .000                                                                             2) 2.007                                                                            3) .000                                                                              4) .000                                       R .500                                                                              ANG                                                                              -6.000                                                                            1) .000                                                                             2) 2.027                                                                            3) .000                                                                              4) .000                                       __________________________________________________________________________    Slope dx/da of Focus Cam at Wide-angle End (28.8 mm) in Second                __________________________________________________________________________    Embodiment                                                                    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) -.208                                                                            3) .000                                                                              4) .000                                       R 10.000                                                                            ANG                                                                              -.207                                                                             1) .000                                                                             2) -.204                                                                            3) .000                                                                              4) .000                                       R 5.000                                                                             ANG                                                                              -.420                                                                             1) .000                                                                             2) -.199                                                                            3) .000                                                                              4) .000                                       R 3.000                                                                             ANG                                                                              -.715                                                                             1) .000                                                                             2) -.192                                                                            3) .000                                                                              4) .000                                       R 2.000                                                                             ANG                                                                              -1.104                                                                            1) .000                                                                             2) -.185                                                                            3) .000                                                                              4) .000                                       R 1.000                                                                             ANG                                                                              -2.416                                                                            1) .000                                                                             2) -.161                                                                            3) .000                                                                              4) .000                                       R .700                                                                              ANG                                                                              -3.761                                                                            1) .000                                                                             2) -.140                                                                            3) .000                                                                              4) .000                                       R .500                                                                              ANG                                                                              -6.000                                                                            1) .000                                                                             2) -.114                                                                            3) .000                                                                              4) .000                                       __________________________________________________________________________    Conversion Coefficient γ.sub.a Associated With Direction of             Rotation at Wide-angle End                                                    (28.8 mm) in Second Embodiment                                                __________________________________________________________________________    R .000                                                                              ANG                                                                              .000                                                                              1) .000                                                                             2) -.406                                                                            3) .000                                                                              4) .000                                       R 10.000                                                                            ANG                                                                              -.207                                                                             1) .000                                                                             2) -.399                                                                            3) .000                                                                              4) .000                                       R 5.000                                                                             ANG                                                                              -.420                                                                             1) .000                                                                             2) -.391                                                                            3) .000                                                                              4) .000                                       R 3.000                                                                             ANG                                                                              -.715                                                                             1) .000                                                                             2) -.378                                                                            3) .000                                                                              4) .000                                       R 2.000                                                                             ANG                                                                              -1.104                                                                            1) .000                                                                             2) -.364                                                                            3) .000                                                                              4) .000                                       R 1.000                                                                             ANG                                                                              -2.416                                                                            1) .000                                                                             2) -.320                                                                            3) .000                                                                              4) .000                                       R .700                                                                              ANG                                                                              -3.761                                                                            1) .000                                                                             2) -.282                                                                            3) .000                                                                              4) .000                                       R .500                                                                              ANG                                                                              -6.000                                                                            1) .000                                                                             2) -.231                                                                            3) .000                                                                              4) .000                                       __________________________________________________________________________     Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.04,        γ.sub.aR /γ.sub.a0 = 0.57                                    

                                      TABLE 22                                    __________________________________________________________________________    Amount DX (mm) of Movement for Focusing in Direction of Optical Axis at       Middle                                                                        Position (50.0 mm) in Second Embodiment                                       __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              .000                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.206                                                                             1)                                                                              .000                                                                             2)                                                                              .077                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.419                                                                             1)                                                                              .000                                                                             2)                                                                              .154                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.713                                                                             1)                                                                              .000                                                                             2)                                                                              .257                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.101                                                                            1)                                                                              .000                                                                             2)                                                                              .385                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.417                                                                            1)                                                                              .000                                                                             2)                                                                              .770                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.775                                                                            1)                                                                              .000                                                                             2)                                                                              1.103                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.000                                                                            1)                                                                              .000                                                                             2)                                                                              1.552                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________    Imaging Magnification β.sub.K of Lens Units at Middle Position (50.0     mm) in Second                                                                 Embodiment                                                                    __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              -.366                                                                             3)                                                                              20.985                                                                            4)                                                                              -.092                                        R  10.000                                                                            ANG                                                                              -.206                                                                             1)                                                                              -.007                                                                            2)                                                                              -.361                                                                             3)                                                                              20.985                                                                            4)                                                                              -.092                                        R  5.000                                                                             ANG                                                                              -.419                                                                             1)                                                                              -.015                                                                            2)                                                                              -.355                                                                             3)                                                                              20.985                                                                            4)                                                                              -.092                                        R  3.000                                                                             ANG                                                                              -.713                                                                             1)                                                                              -.025                                                                            2)                                                                              -.347                                                                             3)                                                                              20.985                                                                            4)                                                                              -.092                                        R  2.000                                                                             ANG                                                                              -1.101                                                                            1)                                                                              -.039                                                                            2)                                                                              -.338                                                                             3)                                                                              20.985                                                                            4)                                                                              -.092                                        R  1.000                                                                             ANG                                                                              -2.417                                                                            1)                                                                              -.086                                                                            2)                                                                              -.309                                                                             3)                                                                              20.985                                                                            4)                                                                              -.092                                        R  .700                                                                              ANG                                                                              -3.775                                                                            1)                                                                              -.135                                                                            2)                                                                              -.284                                                                             3)                                                                              20.985                                                                            4)                                                                              -.092                                        R  .500                                                                              ANG                                                                              -6.000                                                                            1)                                                                              -.218                                                                            2)                                                                              -.251                                                                             3)                                                                              20.985                                                                            4)                                                                              -.092                                        __________________________________________________________________________    Conversion Coefficient γ.sub.x Associated With Direction of Optical     Axis at Middle Position                                                       (50.0 mm) in Second Embodiment                                                __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              3.242                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.206                                                                             1)                                                                              .000                                                                             2)                                                                              3.258                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.419                                                                             1)                                                                              .000                                                                             2)                                                                              3.273                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.713                                                                             1)                                                                              .000                                                                             2)                                                                              3.294                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.101                                                                            1)                                                                              .000                                                                             2)                                                                              3.318                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.417                                                                            1)                                                                              .000                                                                             2)                                                                              3.388                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.775                                                                            1)                                                                              .000                                                                             2)                                                                              3.443                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.000                                                                            1)                                                                              .000                                                                             2)                                                                              3.510                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________    Slope dx/da of Focus Cam at Middle Position (50.0 mm) in Second               __________________________________________________________________________    Embodiment                                                                    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              -.381                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.206                                                                             1)                                                                              .000                                                                             2)                                                                              -.368                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.419                                                                             1)                                                                              .000                                                                             2)                                                                              -.356                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.713                                                                             1)                                                                              .000                                                                             2)                                                                              -.340                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.101                                                                            1)                                                                              .000                                                                             2)                                                                              -.321                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.417                                                                            1)                                                                              .000                                                                             2)                                                                              -.267                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.775                                                                            1)                                                                              .000                                                                             2)                                                                              -.226                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.000                                                                            1)                                                                              .000                                                                             2)                                                                              -.179                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________    Conversion Coefficient γ.sub.a Associated With Direction of             Rotation at Middle Position                                                   (50.0 mm) in Second Embodiment                                                __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              -1.235                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.206                                                                             1)                                                                              .000                                                                             2)                                                                              -1.200                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.419                                                                             1)                                                                              .000                                                                             2)                                                                              -1.165                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.713                                                                             1)                                                                              .000                                                                             2)                                                                              -1.121                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.101                                                                            1)                                                                              .000                                                                             2)                                                                              -1.067                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.417                                                                            1)                                                                              .000                                                                             2)                                                                              -.903                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.775                                                                            1)                                                                              .000                                                                             2)                                                                              -.777                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.000                                                                            1)                                                                              .000                                                                             2)                                                                              -.629                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________     Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.08,        γ.sub.aR /γ.sub.a0 = 0.51                                    

                                      TABLE 23                                    __________________________________________________________________________    Amount DX (mm) of Movement for Focusing in Direction of Optical Axis at       Telephoto                                                                     End (103.0 mm) in Second Embodiment                                           __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              .000                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.206                                                                             1)                                                                              .000                                                                             2)                                                                              .350                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.420                                                                             1)                                                                              .000                                                                             2)                                                                              .669                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.715                                                                             1)                                                                              .000                                                                             2)                                                                              1.057                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.104                                                                            1)                                                                              .000                                                                             2)                                                                              1.496                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.416                                                                            1)                                                                              .000                                                                             2)                                                                              2.611                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.761                                                                            1)                                                                              .000                                                                             2)                                                                              3.414                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.000                                                                            1)                                                                              .000                                                                             2)                                                                              4.356                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________    Imaging Magnification β.sub.K of Lens Units at Telephoto End (103.0      mm) in Second                                                                 Embodiment                                                                    __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              -.652                                                                             3)                                                                              10.590                                                                            4)                                                                              -.212                                        R  10.000                                                                            ANG                                                                              -.206                                                                             1)                                                                              -.007                                                                            2)                                                                              -.626                                                                             3)                                                                              10.590                                                                            4)                                                                              -.212                                        R  5.000                                                                             ANG                                                                              -.420                                                                             1)                                                                              -.015                                                                            2)                                                                              -.602                                                                             3)                                                                              10.590                                                                            4)                                                                              -.212                                        R  3.000                                                                             ANG                                                                              -.715                                                                             1)                                                                              -.025                                                                            2)                                                                              -.573                                                                             3)                                                                              10.590                                                                            4)                                                                              -.212                                        R  2.000                                                                             ANG                                                                              -1.104                                                                            1)                                                                              -.039                                                                            2)                                                                              -.541                                                                             3)                                                                              10.590                                                                            4)                                                                              -.212                                        R  1.000                                                                             ANG                                                                              -2.416                                                                            1)                                                                              -.087                                                                            2)                                                                              -.457                                                                             3)                                                                              10.590                                                                            4)                                                                              -.212                                        R  .700                                                                              ANG                                                                              -3.761                                                                            1)                                                                              -.138                                                                            2)                                                                              -.397                                                                             3)                                                                              10.590                                                                            4)                                                                              -.212                                        R  .500                                                                              ANG                                                                              -6.000                                                                            1)                                                                              -.228                                                                            2)                                                                              -.327                                                                             3)                                                                              10.590                                                                            4)                                                                              -.212                                        __________________________________________________________________________    Conversion Coefficient γ.sub.x Associated With Direction of Optical     Axis at Telephoto End                                                         (103.0 mm) in Second Embodiment                                               __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              2.883                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.206                                                                             1)                                                                              .000                                                                             2)                                                                              3.051                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.420                                                                             1)                                                                              .000                                                                             2)                                                                              3.198                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.715                                                                             1)                                                                              .000                                                                             2)                                                                              3.368                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.104                                                                            1)                                                                              .000                                                                             2)                                                                              3.552                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.416                                                                            1)                                                                              .000                                                                             2)                                                                              3.968                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.761                                                                            1)                                                                              .000                                                                             2)                                                                              4.225                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.000                                                                            1)                                                                              .000                                                                             2)                                                                              4.481                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________    Slope dx/da of Focus Cam at Telephoto End (103.0 mm) in Second                __________________________________________________________________________    Embodiment                                                                    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              -1.829                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.206                                                                             1)                                                                              .000                                                                             2)                                                                              -1.585                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.420                                                                             1)                                                                              .000                                                                             2)                                                                              -1.405                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.715                                                                             1)                                                                              .000                                                                             2)                                                                              -1.226                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.104                                                                            1)                                                                              .000                                                                             2)                                                                              -1.047                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.416                                                                            1)                                                                              .000                                                                             2)                                                                              -.695                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.761                                                                            1)                                                                              .000                                                                             2)                                                                              -.514                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.000                                                                            1)                                                                              .000                                                                             2)                                                                              -.345                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________    Conversion Coefficient γ.sub.a Associated With Direction of             Rotation at Telephoto End                                                     (103.0 mm) in Second Embodiment                                               __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              -5.274                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.206                                                                             1)                                                                              .000                                                                             2)                                                                              -4.835                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.420                                                                             1)                                                                              .000                                                                             2)                                                                              -4.494                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.715                                                                             1)                                                                              .000                                                                             2)                                                                              -4.130                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.104                                                                            1)                                                                              .000                                                                             2)                                                                              -3.719                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.416                                                                            1)                                                                              .000                                                                             2)                                                                              -2.760                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.761                                                                            1)                                                                              .000                                                                             2)                                                                              -2.173                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.000                                                                            1)                                                                              .000                                                                             2)                                                                              -1.548                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________     Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.55,        γ.sub.aR /γ.sub.a0 = 0.29                                    

As can be seen from Tables 21, 22, and 23, at each focal length, theconversion coefficient γ_(x) associated with the direction of theoptical axis increases but the value of the slope (dx/da) of the focuscam decreases as the photographing distance becomes closer to theclosest distance. Therefore, as can be seen from these tables, the valueof the conversion coefficient γ_(a) associated with the direction ofrotation, which is defined as the product of the conversion coefficientγ_(x) and the slope (dx/da) of the focus cam, decreases as thephotographing distance becomes closer to the closest distance by theinfluence of the slope (dx/da) of the focus cam. From Tables 21, 22, and23, the rate of change, from the infinity in-focus position to theclosest in-focus position, of the conversion coefficient γ_(a)associated with the direction of rotation is ×0.57 at the wide-angle end(F=28.8), ×0.51 at the middle position (F=50.0), and x0.29 at thetelephoto end (F=103.0). When the number N of divisions of the focusrange upon a change in conversion coefficient γ_(a) in the secondembodiment is calculated using formula (a), and is compared with that inthe embodiment of Japanese Patent Application Laid-Open No. 5-142475,the numbers N_(W), N_(M), and N_(T) of divisions at the wide-angle end,middle position, and telephoto end respectively have the followingvalues:

Embodiment of Japanese Patent Application Laid-Open No. 5-142475

    N.sub.W >9.3 N.sub.M >10.1 N.sub.T >8.1

Second Embodiment

    N.sub.W >3.1 N.sub.M >3.7 N.sub.T >6.7

Therefore, as can be seen from the above comparison, although the ratio(Δx_(TR) /Δx_(WR)) between the amounts Δx_(TR) and Δx_(WR) of movement,in the direction of the optical axis, of the focusing lens unit requiredfor focusing from the infinity position to the closest distance positionat the wide-angle end and the telephoto end in the first embodiment islarger than that in the embodiment of Japanese Patent ApplicationLaid-Open No. 5-142475 (the embodiment of Japanese Patent ApplicationLaid-Open No. 5-142475: 3.94; the first embodiment: 4.69), the values ofthe numbers N of divisions become small.

As described above, in the second embodiment as well, since the rate ofchange of the conversion coefficient γ_(a) associated with the directionof rotation is smaller than that in the conventional system, the valuesof the numbers N of divisions become small. For this reason, the numberof data of the conversion coefficient γ_(a) and the correctioncoefficient μ can be reduced, and the storage capacity can besuppressed.

Tables 24, 25, and 26 summarize the calculation results of theconversion coefficient K_(a) and the correction coefficient μ at thewide-angle end (F=28.8), middle position (F=50.0), and telephoto end(F=103.0) according to the second embodiment. The arrangements of thetables and reference symbols are the same as those in the firstembodiment. The position of the focusing lens in the first pair in theupper two tables in each of Tables 24, 25, and 26, i.e., in the thirdand fourth columns is (R, ANGLE)=(0.0, 0.0), and it indicates that thisposition corresponds to the infinity corresponding position. Similarly,the position of the focusing lens in the fourth pair in the lower twotables in each of Tables 24, 25, and 26, i.e., in the ninth and tenthcolumns is (R, ANGLE)=(0.5, -6.0), and it indicates that this positioncorresponds to the closest in-focus (R=0.5 m) corresponding position.

                                      TABLE 24                                    __________________________________________________________________________    Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associated        with Direction of Rotation and Correction Coefficient μ: (l) at            Wide-angle End (28.8 mm) of Second Embodiment                                 f = 28.8 mm                                                                   (R,ANGLE) =                                                                           .000                                                                             .000                                                                              10.000                                                                            -.207                                                                             5.000                                                                            -.420                                                                             3.000                                                                            -.715                                        __________________________________________________________________________    POS                                                                              R    r  rs  r   rs  r  rs  r  rs                                           __________________________________________________________________________    1  .000 -.406                                                                            .000    -.402  -.397  -.389                                        2  10.000  -.404                                                                             -.399                                                                             .000   -.394  -.386                                        3  5.000   -.402   -.397                                                                             -.391                                                                            .000   -.383                                        4  3.000   -.397   -.392  -.386                                                                             -.379                                                                            .000                                         5  2.000   -.392   -.386  -.381  -.373                                        6  1.000   -.374   -.369  -.363  -.356                                        7  .700    -.357   -.352  -.347  -.340                                        8  .500    -.330   -.326  -.321  -.315                                        __________________________________________________________________________    POS                                                                              R    bf l   bf  l   bf l   bf l                                            __________________________________________________________________________    1  .000 .00                                                                              .00 -.08                                                                              14.06                                                                             -.17                                                                             11.09                                                                             -.28                                                                             10.15                                        2  10.000                                                                             .08                                                                              16.26                                                                             .00 .00 -.08                                                                             9.92                                                                              -.20                                                                             9.82                                         3  5.000                                                                              .17                                                                              14.41                                                                             .08 11.48                                                                             .00                                                                              .00 -.11                                                                             10.00                                        4  3.000                                                                              .28                                                                              12.64                                                                             .20 10.56                                                                             .11                                                                              9.70                                                                              .00                                                                              .00                                          5  2.000                                                                              .43                                                                              11.92                                                                             .35 10.52                                                                             .26                                                                              10.13                                                                             .15                                                                              10.50                                        6  1.000                                                                              .90                                                                              11.28                                                                             .81 10.57                                                                             .73                                                                              10.36                                                                             .61                                                                              10.34                                        7  .700 1.34                                                                             10.94                                                                             1.25                                                                              10.43                                                                             1.16                                                                             10.23                                                                             1.03                                                                             10.09                                        8  .500 1.98                                                                             10.60                                                                             1.89                                                                              10.22                                                                             1.79                                                                             10.03                                                                             1.66                                                                             9.84                                         __________________________________________________________________________    (R,ANGLE) =                                                                           2.000                                                                            -1.104                                                                            1.000                                                                             -2.416                                                                            .700                                                                             -3.761                                                                            .500                                                                             -6.000                                       __________________________________________________________________________    POS                                                                              R    r  rs  r   rs  r  rs  r  rs                                           __________________________________________________________________________    1  .000    -.379   -.350  -.324  -.288                                        2  l0.000  -.376   -.347  -.322  -.286                                        3  5.000   -.373   -.345  -.319  -.284                                        4  3.000   -.369   -.341  -.316  -.280                                        5  2.000                                                                              -.364                                                                            .000    -.336  -.311  -.276                                        6  1.000   -.348                                                                             -.320                                                                             .000   -.296  -.263                                        7  .700    -.331   -.305                                                                             -.282                                                                            .000   -.250                                        8  .500    -.307   -.282  -.260                                                                             -.231                                                                            .000                                         __________________________________________________________________________    POS                                                                              R    bf l   bf  l   bf l   bf l                                            __________________________________________________________________________    1  .000 -.42                                                                             10.12                                                                             -.85                                                                              9.11                                                                              -1.22                                                                            8.08                                                                              -1.73                                                                            6.93                                         2  10.000                                                                             -.34                                                                             10.04                                                                             -.77                                                                              9.08                                                                              -1.14                                                                            8.05                                                                              -1.66                                                                            6.91                                         3  5.000                                                                              -.26                                                                             10.18                                                                             -.69                                                                              9.08                                                                              -1.07                                                                            8.03                                                                              -1.58                                                                            6.90                                         4  3.000                                                                              -.14                                                                             10.30                                                                             -.58                                                                              9.05                                                                              -.96                                                                             8.00                                                                              -1.48                                                                            6.88                                         5  2.000                                                                              .00                                                                              .00 -.44                                                                              8.99                                                                              -.83                                                                             7.95                                                                              -1.35                                                                            6.85                                         6  1.000                                                                              .46                                                                              9.96                                                                              .00 .00 -.40                                                                             7.82                                                                              -.94                                                                             6.77                                         7  .700 .88                                                                              9.72                                                                              .41 8.51                                                                              .00                                                                              .00 -.56                                                                             6.71                                         8  .500 1.50                                                                             9.49                                                                              1.01                                                                              8.44                                                                              .58                                                                              7.72                                                                              .00                                                                              .00                                          __________________________________________________________________________     Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.81, K.sub.aR     /γ.sub.aR = 1.25                                                   

                                      TABLE 25                                    __________________________________________________________________________    Conversion Coefficients K.sub.a : (rs), γ.sub.a :                       (r) Associated with Direction of Rotation and Correction                      Coefficient μ: (l) at Middle Position (50.0 mm)                            of Second Embodiment                                                          f = 50.0 mm                                                                   (R,ANGLE) =                                                                          .000                                                                              .000                                                                              10.000                                                                            -.206                                                                             5.000                                                                             -.419                                                                             3.000                                                                             -.713                                      __________________________________________________________________________    POS                                                                              R   r   rs  r   rs  r   rs  r   rs                                         __________________________________________________________________________    1  .000                                                                              -1.235                                                                            .000    -1.208  -1.181  -1.147                                     2  10.000  -1.227                                                                            -1.200                                                                            .000    -1.173  -1.139                                     3  5.000   -1.218  -1.191                                                                            -1.165                                                                            .000    -1.131                                     4  3.000   -1.206  -1.180  -1.154                                                                            -1.120                                                                            .000                                       5  2.000   -1.192  -1.166  -1.141  -1.108                                     6  1.000   -1.143  -1.118  -1.093  -1.060                                     7  .700    -1.095  -1.070  -1.046  -1.015                                     8  .500    -1.029  -1.006  -.983   -.954                                      __________________________________________________________________________    POS                                                                              R   bf  l   bf  l   bf  l   bf  l                                          __________________________________________________________________________    1  .000                                                                              .00 .00 -.25                                                                              37.15                                                                             -.49                                                                              34.57                                                                             -.82                                                                              34.36                                      2  10.000                                                                            .25 37.38                                                                             .00 .00 -.25                                                                              34.53                                                                             -.58                                                                              34.46                                      3  5.000                                                                             .51 36.89                                                                             .25 33.78                                                                             .00 .00 -.33                                                                              33.94                                      4  3.000                                                                             .86 37.25                                                                             .60 35.81                                                                             .34 37.90                                                                             .00 .00                                        5  2.000                                                                             1.31                                                                              37.73                                                                             1.04                                                                              36.75                                                                             .78 37.55                                                                             .43 37.83                                      6  1.000                                                                             2.76                                                                              37.10                                                                             2.47                                                                              36.03                                                                             2.18                                                                              35.44                                                                             1.81                                                                              33.86                                      7  .700                                                                              4.13                                                                              36.38                                                                             3.82                                                                              35.30                                                                             3.51                                                                              34.49                                                                             3.11                                                                              32.95                                      8  .500                                                                              6.17                                                                              37.03                                                                             5.83                                                                              36.04                                                                             5.49                                                                              35.23                                                                             5.04                                                                              33.91                                      __________________________________________________________________________    (R,ANGLE) =                                                                          2.000                                                                             -1.101                                                                            1.000                                                                             -2.417                                                                            .700                                                                              -3.775                                                                            .500                                                                              -6.000                                     __________________________________________________________________________    POS                                                                              R   r   rs  r   rs  r   rs  r   rs                                         __________________________________________________________________________    1  .000    -1.105  -.983   -.882   -.760                                      2  10.000  -1.098  -.976   -.875   .754                                       3  5.000   -1.090  -.969   -.869   .749                                       4  3.000   -1.080  -.959   -.860   .741                                       5  2.000                                                                             -1.066                                                                            .000    -.946   -.848   .731                                       6  1.000   -1.020                                                                            -.903                                                                             .000    -.810   .700                                       7  .700    .976    -.864                                                                             -.777                                                                             .000    .673                                       8  .500    .917    -.814   -.734                                                                             -.629                                                                             .000                                       __________________________________________________________________________    POS                                                                              R   bf  l   bf  l   bf  l   bf  l                                          __________________________________________________________________________    1  .000                                                                              -1.22                                                                             33.21                                                                             -2.37                                                                             27.06                                                                             -3.33                                                                             24.55                                                                             -4.56                                                                             21.89                                      2  10.000                                                                            -.98                                                                              33.20                                                                             -2.16                                                                             26.92                                                                             -3.13                                                                             24.53                                                                             -4.37                                                                             21.90                                      3  5.000                                                                             -.74                                                                              32.94                                                                             -1.94                                                                             26.75                                                                             -2.92                                                                             24.51                                                                             -4.18                                                                             21.92                                      4  3.000                                                                             -.42                                                                              31.85                                                                             -1.63                                                                             26.48                                                                             -2.63                                                                             24.50                                                                             -3.92                                                                             21.94                                      5  2.000                                                                             .00 .00 -1.25                                                                             26.18                                                                             -2.27                                                                             24.57                                                                             -3.58                                                                             22.00                                      6  1.000                                                                             1.34                                                                              31.34                                                                             .00 .00 -1.11                                                                             25.60                                                                             -2.51                                                                             22.16                                      7  .700                                                                              2.61                                                                              30.85                                                                             1.17                                                                              26.97                                                                             .00 .00 -1.50                                                                             21.23                                      8  .500                                                                              4.49                                                                              32.24                                                                             2.92                                                                              29.55                                                                             1.63                                                                              29.70                                                                             .00 .00                                        __________________________________________________________________________     Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.83, K.sub.aR     /γ.sub.aR = 1.21                                                   

                                      TABLE 26                                    __________________________________________________________________________    Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associated        with                                                                          Direction of Rotation and Correction Coefficient μ: (l) at Telephoto       End                                                                           (103.0 mm) of Second Embodiment                                               f = 103.0 mm                                                                  (R,ANGLE) =                                                                          .000                                                                              .000 10.000                                                                            -.206                                                                              5.000                                                                             -.420                                                                              3.000                                                                             -.715                                   __________________________________________________________________________    POS                                                                              R   r   rs   r   rs   r   rs   r   rs                                      __________________________________________________________________________    1  .000                                                                              -5.270                                                                            .000     -4.867   -4.524   -4.155                                  2  10.000  -5.243                                                                             -4.835                                                                            .000     -4.497   -4.139                                  3  5.000   -5.218   -4.816                                                                             -4.493                                                                            .000     -4.138                                  4  3.000   -5.217   -4.823   -4.502                                                                             -4.128                                                                            .000                                    5  2.000   -5.216   -4.819   -4.490   -4.110                                  6  1.000   -5.212   -4.798   -4.451   -4.058                                  7  .700    -5.198   -4.764   -4.402   -3.996                                  8  .500    -5.161   -4.695   -4.311   -3.887                                  __________________________________________________________________________    POS                                                                              R   bf  l    bf  l    bf  l    bf  l                                       __________________________________________________________________________    1  .000                                                                              .00 .00  -1.02                                                                             146.74                                                                             -1.90                                                                             275.20                                                                             -2.97                                                                             443.13                                  2  10.000                                                                            1.08                                                                              204.63                                                                             .00 .00  -.96                                                                              896.68                                                                             -2.11                                                                             760.19                                  3  5.000                                                                             2.19                                                                              221.01                                                                             1.03                                                                              276.55                                                                             .00 .00  -1.22                                                                             494.64                                  4  3.000                                                                             3.73                                                                              369.34                                                                             2.46                                                                              1022.53                                                                            1.33                                                                              -668.50                                                                            .00 .00                                     5  2.000                                                                             5.76                                                                              557.10                                                                             4.33                                                                              1376.19                                                                            3.07                                                                              4825.30                                                                            1.60                                                                              371.39                                  6  1.000                                                                             12.59                                                                             1138.58                                                                            10.60                                                                             1391.91                                                                            8.88                                                                              948.72                                                                             6.90                                                                              406.05                                  7  .700                                                                              19.55                                                                             1423.88                                                                            16.94                                                                             1156.35                                                                            14.71                                                                             724.98                                                                             12.17                                                                             380.60                                  8  .500                                                                              30.96                                                                             1486.85                                                                            27.20                                                                             942.21                                                                             24.06                                                                             595.02                                                                             20.54                                                                             352.62                                  __________________________________________________________________________    (R,ANGLE) =                                                                          2.000                                                                             -1.104                                                                             1.000                                                                             -2.416                                                                             .700                                                                              -3.761                                                                             .500                                                                              -6.000                                  __________________________________________________________________________    POS                                                                              R   r   rs   r   rs   r   rs   r   rs                                      __________________________________________________________________________    1  .000    -3.768   -2.909   -2.383   -1.849                                  2  10.000  -3.754   -2.896   -2.370   -1.837                                  3  5.000   -3.747   -2.885   -2.358   -1.826                                  4  3.000   -3.732   -2.868   -2.341   -1.811                                  5  2.000                                                                             -3.717                                                                            .000     -2.846   -2.319   -1.790                                  6  1.000   -3.651                                                                             -2.759                                                                            .000     -2.244   -1.723                                  7  .700    -3.579   -2.690                                                                             -2.173                                                                            .000     -1.657                                  8  .500    -3.459   -2.563   -2.051                                                                             -1.548                                                                            .000                                    __________________________________________________________________________    POS                                                                              R   bf  l    bf  l    bf  l    bf  l                                       __________________________________________________________________________    1  .000                                                                              -4.16                                                                             304.61                                                                             -7.03                                                                             129.28                                                                             -8.96                                                                             92.55                                                                              -11.09                                                                            57.17                                   2  10.000                                                                            -3.37                                                                             343.34                                                                             -6.40                                                                             129.20                                                                             -8.43                                                                             92.62                                                                              -10.65                                                                            57.03                                   3  5.000                                                                             -2.56                                                                             319.55                                                                             -5.76                                                                             126.54                                                                             -7.88                                                                             92.08                                                                              -10.19                                                                            56.76                                   4  3.000                                                                             -1.45                                                                             352.62                                                                             -4.88                                                                             123.89                                                                             -7.13                                                                             91.72                                                                              -9.57                                                                             56.46                                   5  2.000                                                                             .00 .00  -3.73                                                                             118.89                                                                             -6.16                                                                             91.24                                                                              -8.77                                                                             56.05                                   6  1.000                                                                             4.79                                                                              269.34                                                                             .00 .00  -3.02                                                                             91.90                                                                              -6.18                                                                             54.70                                   7  .700                                                                              9.51                                                                              256.75                                                                             3.62                                                                              143.56                                                                             .00 .00  -3.71                                                                             52.75                                   8  .500                                                                              16.93                                                                             243.43                                                                             9.19                                                                              129.15                                                                             4.59                                                                              81.82                                                                              .00 .00                                     __________________________________________________________________________     Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.98, K.sub.aR     /γ.sub.aR = 1.19                                                   

The calculation results of the rate of change of K_(a) with respect toγ_(a) at the infinity in-focus arrangement and the closest in-focusarrangement at the wide-angle end, middle position, and telephoto end inthe embodiment of Japanese Patent Application Laid-Open No. 5-142475 andin the second embodiment of the present invention are as follows.

    ______________________________________                                        Embodiment of Japanese Patent Application Laid-Open No. 5-142475                        Infinity Arrangement                                                                      Closest Arrangement                                               K.sub.aO /γ.sub.aO                                                                  K.sub.aR /γ.sub.aR                                ______________________________________                                        Wide-angle End                                                                            2.75          0.44                                                (F = 36.0)                                                                    Middle Position                                                                           3.36          0.43                                                (F = 50.0)                                                                    Telephoto End                                                                             3.80          0.43                                                (F = 103.0)                                                                   Second Embodiment                                                             Wide-angle End                                                                            0.81          1.25                                                (F = 28.8)                                                                    Middle Position                                                                           0.83          1.21                                                (F = 50.0)                                                                    Telephoto End                                                                             0.98          1.19                                                (F = 103.0)                                                                   ______________________________________                                    

As described above, in the second embodiment as well, since the rate ofchange of K_(a) with respect to γ_(a) is small as compared to theconventional system, the contribution of the correction term (ΔBf/μ) inK_(a) =γ_(a) (1-ΔBf/μ) can be reduced. For this reason, an error of theconversion coefficient K_(a) calculated based on γ_(a) and μ or an errorfrom the actual lens driving amount Δa obtained when only one pair of aconversion coefficient γ_(a) value and a correction coefficient μ valueare set can be reduced.

Next, in the embodiment of Japanese Patent Application Laid-Open No.5-142475 and the second embodiment of the present invention, when thelens driving amounts upon focusing from the infinity in-focus lensarrangement to the closest distance object and upon focusing from theclosest in-focus lens arrangement to the infinity object at thewide-angle end, middle position, and telephoto end are calculated fromΔa=ΔBf/ γ_(a) (1-ΔBf/μ!, and errors from the actual lens driving amountsare then calculated, the following values are obtained. Note that thevalue of the correction coefficient p upon focusing from the infinityin-focus lens arrangement to the closest distance object adopts a valueat the object distance (POS-5), and the value of the correctioncoefficient μ upon focusing from the closest in-focus lens arrangementto the infinity object adopts a value at the object distance (POS-4).

    ______________________________________                                        Embodiment of Japanese Patent Application Laid-Open No. 5-142475                       Infinity Arrangement →                                                              Closest Arrangement →                                     Closest In-focus State                                                                     Infinity In-focus State                                 ______________________________________                                        Wide-angle End                                                                           -4.4%          -13.0%                                              (F = 36.0)                                                                    Middle Position                                                                          -11.8%         -12.0%                                              (F = 50.0)                                                                    Telephoto End                                                                            -12.6%         -14.6%                                              (F = 103.0)                                                                   Second Embodiment                                                             Wide-angle End                                                                           -2.5%          -0.3%                                               (F = 28.8)                                                                    Middle Position                                                                          -0.5%          0.0%                                                (F = 50.0)                                                                    Telephoto End                                                                            3.7%           -0.2%                                               (F = 103.0)                                                                   ______________________________________                                    

As described above, in the second embodiment as well, even when only apair of a conversion coefficient γ_(a) value and a correctioncoefficient μ value are set for a given lens arrangement range, an errorbetween the conversion coefficient K_(a) calculated from γ_(a) and μ andthe lens driving amount Δa for focusing becomes small as compared to theconventional system, and focusing can be realized with higher accuracy.

Table 27 summarizes the amount (ANGLE DA) of rotation for focusing uponmanual focusing using the focus cam (the middle table in Table 19) ofthe second embodiment, the amount DX (mm) of movement, in the directionof the optical axis, of the focusing lens unit corresponding to theamount of rotation for focusing, and the displacement amount Bf (mm) ofthe imaging point when the amount (DX) of movement in the direction ofthe optical axis is given.

Note that the arrangement of the table and reference symbols are thesame as those in the first embodiment. The upper table in Table 27summarizes the displacement amount (Bf) of the imaging pointcorresponding to the photographing distances (R=5.0, 3.0, 2.0, 1.0, 0.7,and 0.5 m) in the respective zooming states of the focal lengths(F=28.8, 35.0, 50.0, 70.0, 85.0, and 103.0 mm), and the middle tablesummarizes the values of the amount (ANGLE DA) of rotation for focusingrequired for attaining an optimal in-focus state with respect to therespective photographing distances. The lower table summarizes theamounts (DX) of movement, in the direction of the optical axis, of therespective lens units corresponding to the amount (ANGLE DA) of rotationfor focusing in association with the focal lengths and photographingdistances.

                                      TABLE 27                                    __________________________________________________________________________    Displacement Amount Bf (mm) of Imaging Point and Amount DX                    (mm) of movement for focusing in Second Embodiment                                      0.50 m                                                                             0.70 m                                                                             1.00 m                                                                            2.00 m                                                                            3.00 m                                                                             5.00 m                                       __________________________________________________________________________        28.800 Bf                                                                           .000                                                                               .000                                                                               .000                                                                              .000                                                                               .000                                                                               .000                                            35.000 Bf                                                                           .000                                                                               .003                                                                               .007                                                                              .008                                                                               .006                                                                               .004                                            50.000 Bf                                                                           .000                                                                               .011                                                                               .001                                                                              -.003                                                                             -.002                                                                              -.002                                            70.000 Bf                                                                           .000                                                                               -.019                                                                              -.024                                                                             -.015                                                                             -.010                                                                              -.006                                            85.000 Bf                                                                           .000                                                                               -.015                                                                              -.011                                                                             -.013                                                                             -.013                                                                              -.008                                           103.000 Bf                                                                           .000                                                                               .000                                                                               .000                                                                              .000                                                                               .000                                                                               .000                                           ANGLE DA                                                                            -6.000                                                                             -3.761                                                                             -2.416                                                                            -1.104                                                                             -.715                                                                              -.420                                        F   28.800 DX                                                                           .000                                                                               .928                                                                               .000                                                                              .000 R                                                                            0.50 m                                            F   35.000 DX                                                                           .000                                                                               1.086                                                                              .000                                                                              .000 R                                                                            0.50 m                                            F   50.000 DX                                                                           .000                                                                               1.552                                                                              .000                                                                              .000 R                                                                            0.50 m                                            F   70.000 DX                                                                           .000                                                                               2.432                                                                              .000                                                                              .000 R                                                                            0.50 m                                            F   85.000 DX                                                                           .000                                                                               3.232                                                                              .000                                                                              .000 R                                                                            0.50 m                                            F  103.000 DX                                                                           .000                                                                               4.356                                                                              .000                                                                              .000 R                                                                            0.50 m                                            F   28.800 DX                                                                           .000                                                                               .645                                                                               .000                                                                              .000 R                                                                            0.70 m                                            F   35.000 DX                                                                           .000                                                                               .757                                                                               .000                                                                              .000 R                                                                            0.70 m                                            F   50.000 DX                                                                           .000                                                                               1.100                                                                              .000                                                                              .000 R                                                                            0.70 m                                            F   70.000 DX                                                                           .000                                                                               1.791                                                                              .000                                                                              .000 R                                                                            0.70 m                                            F   85.000 DX                                                                           .000                                                                               2.447                                                                              .000                                                                              .000 R                                                                            0.70 m                                            F  103.000 DX                                                                           .000                                                                               3.414                                                                              .000                                                                              .000 R                                                                            0.70 m                                            F   28.800 DX                                                                           .000                                                                               .443                                                                               .000                                                                              .000 R                                                                            1.00 m                                            F   35.000 DX                                                                           .000                                                                               .520                                                                               .000                                                                              .000 R                                                                            1.00 m                                            F   50.000 DX                                                                           .000                                                                               .770                                                                               .000                                                                              .000 R                                                                            1.00 m                                            F   70.000 DX                                                                           .000                                                                               1.290                                                                              .000                                                                              .000 R                                                                            1.00 m                                            F   85.000 DX                                                                           .000                                                                               1.804                                                                              .000                                                                              .000 R                                                                            1.00 m                                            F  103.000 DX                                                                           .000                                                                               2.611                                                                              .000                                                                              .000 R                                                                            1.00 m                                            F   28.800 DX                                                                           .000                                                                               .217                                                                               .000                                                                              .000 R                                                                            2.00 m                                            F   35.000 DX                                                                           .000                                                                               .254                                                                               .000                                                                              .000 R                                                                            2.00 m                                            F   50.000 DX                                                                           .000                                                                               .386                                                                               .000                                                                              .000 R                                                                            2.00 m                                            F   70.000 DX                                                                           .000                                                                               .670                                                                               .000                                                                              .000 R                                                                            2.00 m                                            F   85.000 DX                                                                           .000                                                                               .974                                                                               .000                                                                              .000 R                                                                            2.00 m                                            F  103.000 DX                                                                           .000                                                                               1.496                                                                              .000                                                                              .000 R                                                                            2.00 m                                            F   28.800 DX                                                                           .000                                                                               .143                                                                               .000                                                                              .000 R                                                                            3.00 m                                            F   35.000 DX                                                                           .000                                                                               .168                                                                               .000                                                                              .000 R                                                                            3.00 m                                            F   50.000 DX                                                                           .000                                                                               .257                                                                               .000                                                                              .000 R                                                                            3.00 m                                            F   70.000 DX                                                                           .000                                                                               .453                                                                               .000                                                                              .000 R                                                                            3.00 m                                            F   85.000 DX                                                                           .000                                                                               .670                                                                               .000                                                                              .000 R                                                                            3.00 m                                            F  103.000 DX                                                                           .000                                                                               1.057                                                                              .000                                                                              .000 R                                                                            3.00 m                                            F   28.800 DX                                                                           .000                                                                               .086                                                                               .000                                                                              .000 R                                                                            5.00 m                                            F   35.000 DX                                                                           .000                                                                               .100                                                                               .000                                                                              .000 R                                                                            5.00 m                                            F   50.000 DX                                                                           .000                                                                               .155                                                                               .000                                                                              .000 R                                                                            5.00 m                                            F   70.000 DX                                                                           .000                                                                               .275                                                                               .000                                                                              .000 R                                                                            5.00 m                                            F   85.000 DX                                                                           .000                                                                               .413                                                                               .000                                                                              .000 R                                                                            5.00 m                                            F  103.000 DX                                                                           .000                                                                               .669                                                                               .000                                                                              .000 R                                                                            5.00 m                                            __________________________________________________________________________

As can be seen from Table 27, in the zoom lens of the second embodiment,so-called manual focusing can be attained since the displacement amountsof the imaging point at the respective focal lengths and photographingdistances are very small, and fall within the depth of focusindependently of the zooming state and photographing distance.

Third Embodiment!

The third embodiment is directed to a zoom lens which has a four-unitarrangement, i.e., positive, negative, positive, and positive lensunits, and attains focusing by a negative second lens unit. In this zoomlens, the rotation amount ratio (a_(F) /a_(Z)) of the rotation amountfor focusing from the infinity in-focus position to the closest in-focusposition (R=0.5 m) to the amount of rotation for zooming from thewide-angle end (F=24.7) to the telephoto end (F=116.5) is set to be-0.65.

Table 28 below summarizes various paraxial data of an optical system anddata for defining the shape of a focus cam according to the thirdembodiment.

The upper table in Table 28 summarizes the focal lengths and principalpoint interval data of the respective lens units of the optical systemcorresponding to the third embodiment in association with six zoomingstates (focal length F=24.7 (1-POS), 35.0 (2-POS), 50.0 (3-POS), 70.0(4-POS), 85.0 (5-POS) and 116.5 mm (6-POS)).

The middle table in Table 28 summarizes spline sample data when theshape of the focus cam in the second lens unit of the third embodiment,which is used for focusing, is expressed by a spline function associatedwith the angle a of rotation of a rotatable lens barrel and the amount xof movement in the direction of the optical axis. In this middle table,(1), (2), (3), and (4) correspond to the first, second, third, andfourth lens units, respectively.

Furthermore, the lower table in Table 28 summarizes the infinityfocusing positions (infinity corresponding positions) at the respectivefocal lengths (F=24.7, 35.0, 50.0, 70.0, 85.0, and 116.5 mm), and theamounts of rotation (amounts of rotation for focusing) upon focusing torespective photographing distances (R=5.0, 3.0, 2.0, 1.0, 0.7, and 0.5m) using the focus cam of the third embodiment. In this table, since theamount of rotation for zooming from the wide-angle end (F=24.7) to thetelephoto end (F=116.5) is set to be 10.0, and the amount of rotationfor focusing from the infinity in-focus position to the closest in-focusposition (R=0.5 m) is set to be -6.5, the rotation amount ratio (a_(F)/a_(Z)) of the amount of rotation for focusing to the amount of rotationfor zooming in the third embodiment is -0.65.

                                      TABLE 28                                    __________________________________________________________________________    Third Embodiment f = 24.7 to 116.5 (Rotation Amount Ratio:                    a.sub.r /a.sub.z = -0.65)                                                     Focal lengths and Principal Point Intervals of Lens Units of Third            Embodiment                                                                              1-POS                                                                             2-POS                                                                             3-POS                                                                             4-POS                                                                             5-POS                                                                              6-POS                                          __________________________________________________________________________            F 24.7000                                                                           35.0000                                                                           50.0000                                                                           70.0000                                                                           85.0000                                                                            116.5000                                       F1 85.3000                                                                            D1                                                                              10.2543                                                                           17.8350                                                                           25.9637                                                                           33.8700                                                                           38.2274                                                                            45.1382                                        F2 -13.2000                                                                           D2                                                                              23.3675                                                                           19.2391                                                                           16.0845                                                                           13.7175                                                                           12.4349                                                                            10.2948                                        F3 36.5000                                                                            D3                                                                              12.9146                                                                           11.5977                                                                            9.4254                                                                            7.8476                                                                            7.3925                                                                             7.7644                                        F4 58.3000                                                                            D4                                                                              52.0486                                                                           60.5902                                                                           69.5534                                                                           77.3756                                                                           81.6671                                                                            87.4532                                        __________________________________________________________________________    Focus Cam Shape (Spline Interpolation Sample Point) Corresponding             to Third Embodiment                                                              ANGLE      (1)                                                                              (2)     (3)                                                                              (4)                                               __________________________________________________________________________    1  -10.0000   .0000                                                                             1.0420 .0000                                                                            .0000                                             2  -6.5000    .0000                                                                             .7829  .0000                                                                            .0000                                             3  -3.9410    .0000                                                                             .5392  .0000                                                                            .0000                                             4  -2.4857    .0000                                                                             .3677  .0000                                                                            .0000                                             5  -1.1175    .0000                                                                             .1786  .0000                                                                            .0000                                             6  -.7209     .0000                                                                             .1179  .0000                                                                            .0000                                             7  -.4216     .0000                                                                             .0702  .0000                                                                            .0000                                             8  -.0000     .0000                                                                             .0000  .0000                                                                            .0000                                             9  3.5000     .0000                                                                             -.7434 .0000                                                                            .0000                                             10 6.0590     .0000                                                                            -1.5883 .0000                                                                            .0000                                             11 7.5143     .0000                                                                            -2.2742 .0000                                                                            .0000                                             12 8.8825     .0000                                                                            -3.1618 .0000                                                                            .0000                                             13 9.2791     .0000                                                                            -3.4870 .0000                                                                            .0000                                             14 9.5784     .0000                                                                            -3.7611 .0000                                                                            .0000                                             15 10.0000    .0000                                                                            -4.2005 .0000                                                                            .0000                                             16 11.0000    .0000                                                                            -5.5000 .0000                                                                            .0000                                             __________________________________________________________________________    Amount of Rotation for Zooming and Amount of Rotation                         for Focusing of Third Embodiment                                              (Rotation Amount Ratio: a.sub.r /a.sub.z = -0.6)                                     Infinity             Amount of                                                Corresponding                                                                            Photographing                                                                           Rotation for                                      Focal Length                                                                         Position   Distance  Focusing                                          __________________________________________________________________________    24.7 mm                                                                               .0000      5.00 m    -.422                                            35.0 mm                                                                              2.2335      3.00 m    -.721                                            50.0 mm                                                                              4.6690      2.00 m   -1.117                                            70.0 mm                                                                              6.9845      1.00 m   -2.486                                            85.0 mm                                                                              8.2090      0.70 m   -3.941                                            116.5 mm                                                                             10.0000     0.50 m   -6.500                                            Condition Corresponding Value (1)                                                                1.25                                                       Condition Corresponding Value (2)                                                                4.42                                                       Condition Corresponding Value (3)                                                               -0.65                                                       Condition Corresponding Value (4)                                                                0.50 (wide-angle end)                                                         0.29 (telephoto end)                                       Condition Corresponding Value (5)                                                                0.75 (wide-angle end)                                                         0.93 (telephoto end)                                       Condition Corresponding Vatue (6)                                                                1.36 (wide-angle end)                                                         1.26 (telephoto end)                                       __________________________________________________________________________

Table 29 below summarizes the numerical value data of the cams of thefocusing lens unit in the third embodiment, which data are calculated byinterpolation based on a spline function on the basis of the sample dataof the focus cam summarized in the middle table in Table 28. Note thatthe meanings of the reference symbols in Table 29 are the same as thosein the first embodiment.

                  TABLE 29                                                        ______________________________________                                        Cam Numerical Value Data of                                                   Focusing Lens Unit in Third Embodiment                                        Focus Cam         Zoom Compensation Cam                                       Numerical Value Data                                                                            Numerical Value Data                                        ANGLE  (2)       F        ANGLE  (2)   F                                      ______________________________________                                        -6.5000                                                                              .7829     .0000                                                        -6.0000                                                                              .7402     .0000                                                        -5.5000                                                                              .6952     .0000                                                        -5.0000                                                                              .6480     .0000                                                        -4.5000                                                                              .5981     .0000                                                        -4.0000                                                                              .5456     .0000                                                        -3.5000                                                                              .4901     .0000                                                        -3.0000                                                                              .4315     .0000                                                        -2.5000                                                                              .3695     .0000                                                        -2.0000                                                                              .3039     .0000                                                        -1.5000                                                                              .2345     .0000                                                        -1.0000                                                                              .1609     .0000                                                        -.5000 .0829     .0000                                                        .0000  .0000     24.7000  .0000  .0000 24.7000                                .5000  -.0875    26.8114  .5000  .7812 26.8114                                1.0000 -.1799    29.0129  1.0000 1.5598                                                                              29.0129                                1.5000 -.2781    31.3321  1.5000 2.3460                                                                              31.3321                                2.0000 -.3827    33.7944  2.0000 3.1482                                                                              33.7944                                2.5000 -.4947    36.4231  2.5000 3.9736                                                                              36.4231                                3.0000 -.6147    39.2326  3.0000 4.8242                                                                              39.2326                                3.5000 -.7434    42.2264  3.5000 5.6971                                                                              42.2264                                4.0000 -.8819    45.4086  4.0000 6.5896                                                                              45.4086                                4.5000 -1.0316   48.8015  4.5000 7.5036                                                                              48.8015                                5.0000 -1.1942   52.4265  5.0000 8.4407                                                                              52.4265                                5.5000 -1.3712   56.3184  5.5000 9.4088                                                                              56.3184                                6.0000 -1.5644   60.5242  6.0000 10.4208                                                                             60.5242                                6.5000 -1.7756   65.0942  6.5000 11.4904                                                                             65.0942                                7.0000 -2.0082   70.1659  7.0000 12.6481                                                                             70.1659                                7.5000 -2.2664   75.8479  7.5000 13.9132                                                                             75.8479                                8.0000 -2.5547   82.1609  8.0000 15.2647                                                                             82.1609                                8.5000 -2.8810   89.1652  8.5000 16.6799                                                                             89.1652                                9.0000 -3.2542   96.9887  9.0000 18.1524                                                                             96.9887                                9.5000 -3.6867   105.9218 9.5000 19.7045                                                                             105.9218                               10.0000                                                                              -4.2005   116.5000 10.0000                                                                              21.3821                                                                             116.5000                               ______________________________________                                    

The left table in Table 29 summarizes the numerical value data of thefocus cam of the third embodiment, and the right table in Table 29summarizes the numerical value data of the zoom compensation cam of thisembodiment. A value obtained by synthesizing the amounts (2) of movementin the direction of the optical axis in the numerical value data of thefocus cam and the zoom compensation cam in the range from the amount ofrotation (ANGLE=0.0) to the amount of rotation (ANGLE=10.0) coincideswith the movement locus of the second lens unit calculated using theparaxial data in the upper table in Table 28.

Tables 30, 31, and 32 below summarize the amount DX (mm) of movement forfocusing, in the direction of the optical axis, of the focusing lensunit, the imaging magnificeations β_(x) of the respective lens units,the conversion coefficient γ_(x) associated with the direction of theoptical axis, the slope (dx/da) of the focus cam, and the conversioncoefficient γ_(a) associated with the direction of rotation at thewide-angle end (F=24.7), the middle position (F=50.0), and the telephotoend (F=116.5) according to the third embodiment, respectively. Thearrangements of the respective tables and the meanings of the referencesymbols are the same as those in the first embodiment.

                                      TABLE 30                                    __________________________________________________________________________    Amount DX (mm) of Movement for Focusing in Direction of Optical Axis at       Wide-angle End (24.7 mm) in Third Embodiment                                  __________________________________________________________________________    R  .000                                                                              ANG .000                                                                              1)                                                                              .000                                                                             2)                                                                              .000                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG -.207                                                                             1)                                                                              .000                                                                             2)                                                                              .035                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG -.422                                                                             1)                                                                              .000                                                                             2)                                                                              .070                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG -.721                                                                             1)                                                                              .000                                                                             2)                                                                              .118                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG -1.117                                                                            1)                                                                              .000                                                                             2)                                                                              .179                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG -2.486                                                                            1)                                                                              .000                                                                             2)                                                                              .368                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG -3.941                                                                            1)                                                                              .000                                                                             2)                                                                              .539                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG -6.500                                                                            1)                                                                              .000                                                                             2)                                                                              .783                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________    Imaging Magnification β.sub.K of Lens Units at Wide-angle End            (24.7 mm) in Third Embodiment                                                 __________________________________________________________________________    R  .000                                                                              ANG .000                                                                              1)                                                                              .000                                                                             2)                                                                              -.213                                                                            3)                                                                              -12.652                                                                           4)                                                                              .107                                         R  10.000                                                                            ANG -.207                                                                             1)                                                                              -.009                                                                            2)                                                                              -.211                                                                            3)                                                                              -12.652                                                                           4)                                                                              .107                                         R  5.000                                                                             ANG -.422                                                                             1)                                                                              -.018                                                                            2)                                                                              -.208                                                                            3)                                                                              -12.652                                                                           4)                                                                              .107                                         R  3.000                                                                             ANG -.721                                                                             1)                                                                              -.030                                                                            2)                                                                              -.205                                                                            3)                                                                              -12.652                                                                           4)                                                                              .107                                         R  2.000                                                                             ANG -1.117                                                                            1)                                                                              -.047                                                                            2)                                                                              -.200                                                                            3)                                                                              -12.652                                                                           4)                                                                              .107                                         R  1.000                                                                             ANG -2.486                                                                            1)                                                                              -.105                                                                            2)                                                                              -.186                                                                            3)                                                                              -12.652                                                                           4)                                                                              .107                                         R  .700                                                                              ANG -3.941                                                                            1)                                                                              -.165                                                                            2)                                                                              -.173                                                                            3)                                                                              -12.652                                                                           4)                                                                              .107                                         R  .500                                                                              ANG -6.500                                                                            1)                                                                              -.270                                                                            2)                                                                              -.154                                                                            3)                                                                              -12.652                                                                           4)                                                                              .107                                         __________________________________________________________________________    Conversion Coefficient γ.sub.x Associated With Direction of Optical     Axis at Wide-angle End                                                        (24.7 mm) in Third Embodiment                                                 __________________________________________________________________________    R  .000                                                                              ANG .000                                                                              1)                                                                              .000                                                                             2)                                                                              1.757                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG -.207                                                                             1)                                                                              .000                                                                             2)                                                                              1.759                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG -.422                                                                             1)                                                                              .000                                                                             2)                                                                              1.761                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG -.721                                                                             1)                                                                              .000                                                                             2)                                                                              1.764                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG -1.117                                                                            1)                                                                              .000                                                                             2)                                                                              1.767                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG -2.486                                                                            1)                                                                              .000                                                                             2)                                                                              1.777                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG -3.941                                                                            1)                                                                              .000                                                                             2)                                                                              1.786                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG -6.500                                                                            1)                                                                              .000                                                                             2)                                                                              1.797                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________    Slope dx/da of Focus Cam at Wide-angle End (24.7 mm) in Third                 __________________________________________________________________________    Embodiment                                                                    R  .000                                                                              ANG .000                                                                              1)                                                                              .000                                                                             2)                                                                              -.170                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG -.207                                                                             1)                                                                              .000                                                                             2)                                                                              -.167                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG -.422                                                                             1)                                                                              .000                                                                             2)                                                                              -.162                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG -.721                                                                             1)                                                                              .000                                                                             2)                                                                              -.156                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG -1.117                                                                            1)                                                                              .000                                                                             2)                                                                              -.149                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG -2.486                                                                            1)                                                                              .000                                                                             2)                                                                              -.128                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG -3.941                                                                            1)                                                                              .000                                                                             2)                                                                              -.109                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG -6.500                                                                            1)                                                                              .000                                                                             2)                                                                              -.083                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________    Conversion Coefficient γ.sub.a Associated With Direction of             Rotation at Wide-angle End                                                    (24.7 mm) in Third Embodiment                                                 __________________________________________________________________________    R  .000                                                                              ANG .000                                                                              1)                                                                              .000                                                                             2)                                                                              -.299                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG -.207                                                                             1)                                                                              .000                                                                             2)                                                                              -.293                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG -.422                                                                             1)                                                                              .000                                                                             2)                                                                              -.286                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG -.721                                                                             1)                                                                              .000                                                                             2)                                                                              -.276                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG -1.117                                                                            1)                                                                              .000                                                                             2)                                                                              -.264                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG -2.486                                                                            1)                                                                              .000                                                                             2)                                                                              -.227                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG -3.941                                                                            1)                                                                              .000                                                                             2)                                                                              -.194                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG -6.500                                                                            1)                                                                              .000                                                                             2)                                                                              -.150                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________     Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.02,        γ.sub.aR /γ.sub.a0 = 0.50                                    

                                      TABLE 31                                    __________________________________________________________________________    Amount DX (mm) of Movement for Focusing in Direction of Optical Axis at       Middle Position (50.0 mm) in Third Embodiment                                 __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              .000                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.206                                                                             1)                                                                              .000                                                                             2)                                                                              .065                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.421                                                                             1)                                                                              .000                                                                             2)                                                                              .130                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.720                                                                             1)                                                                              .000                                                                             2)                                                                              .218                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.117                                                                            1)                                                                              .000                                                                             2)                                                                              .328                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.491                                                                            1)                                                                              .000                                                                             2)                                                                              .663                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.955                                                                            1)                                                                              .000                                                                             2)                                                                              .959                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.500                                                                            1)                                                                              .000                                                                             2)                                                                              1.366                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________    Imaging Magnification β.sub.K of Lens Units at Middle Position (50.0     mm)                                                                           in Third Embodiment                                                           __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              -.286                                                                             3)                                                                              10.614                                                                            4)                                                                              -.193                                        R  10.000                                                                            ANG                                                                              -.206                                                                             1)                                                                              -.009                                                                            2)                                                                              -.281                                                                             3)                                                                              10.614                                                                            4)                                                                              -.193                                        R  5.000                                                                             ANG                                                                              -.421                                                                             1)                                                                              -.018                                                                            2)                                                                              -.276                                                                             3)                                                                              10.614                                                                            4)                                                                              -.193                                        R  3.000                                                                             ANG                                                                              -.720                                                                             1)                                                                              -.031                                                                            2)                                                                              -.270                                                                             3)                                                                              10.614                                                                            4)                                                                              -.193                                        R  2.000                                                                             ANG                                                                              -1.117                                                                            1)                                                                              -.048                                                                            2)                                                                              -.261                                                                             3)                                                                              10.614                                                                            4)                                                                              -.193                                        R  1.000                                                                             ANG                                                                              -2.491                                                                            1)                                                                              -.107                                                                            2)                                                                              -.236                                                                             3)                                                                              10.614                                                                            4)                                                                              -.193                                        R  .700                                                                              ANG                                                                              -3.955                                                                            1)                                                                              -.173                                                                            2)                                                                              -.213                                                                             3)                                                                              10.614                                                                            4)                                                                              -.193                                        R  .500                                                                              ANG                                                                              -6.500                                                                            1)                                                                              -.290                                                                            2)                                                                              -.183                                                                             3)                                                                              10.614                                                                            4)                                                                              -.193                                        __________________________________________________________________________    Conversion Coefficient γ.sub.x Associated With Direction of Optical     Axis at Middle Position                                                       (50.0 mm) in Third Embodiment                                                 __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              3.854                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.206                                                                             1)                                                                              .000                                                                             2)                                                                              3.866                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.421                                                                             1)                                                                              .000                                                                             2)                                                                              3.877                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.720                                                                             1)                                                                              .000                                                                             2)                                                                              3.892                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.117                                                                            1)                                                                              .000                                                                             2)                                                                              3.911                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.491                                                                            1)                                                                              .000                                                                             2)                                                                              3.964                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.955                                                                            1)                                                                              .000                                                                             2)                                                                              4.006                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.500                                                                            1)                                                                              .000                                                                             2)                                                                              4.057                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________    Slope dx/da of Focus Cam at Middle Position (50.0 mm) in Third                __________________________________________________________________________    Embodiment                                                                    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              -.321                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.206                                                                             1)                                                                              .000                                                                             2)                                                                              -.310                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.421                                                                             1)                                                                              .000                                                                             2)                                                                              -.299                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.720                                                                             1)                                                                              .000                                                                             2)                                                                              -.285                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.117                                                                            1)                                                                              .000                                                                             2)                                                                              -.269                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.491                                                                            1)                                                                              .000                                                                             2)                                                                              -.222                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.955                                                                            1)                                                                              .000                                                                             2)                                                                              -.184                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.500                                                                            1)                                                                              .000                                                                             2)                                                                              -.138                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________    Conversion Coefficient γ.sub.a Associated With Direction of             Rotation at Middle Position                                                   (50.0 mm) in Third Embodiment                                                 __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              -1.235                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.206                                                                             1)                                                                              .000                                                                             2)                                                                              -1.198                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.421                                                                             1)                                                                              .000                                                                             2)                                                                              -1.160                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.720                                                                             1)                                                                              .000                                                                             2)                                                                              -1.111                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.117                                                                            1)                                                                              .000                                                                             2)                                                                              -1.052                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.491                                                                            1)                                                                              .000                                                                             2)                                                                              -.879                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.955                                                                            1)                                                                              .000                                                                             2)                                                                              -.737                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.500                                                                            1)                                                                              .000                                                                             2)                                                                              -.558                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________     Condition Corresponding Values: γ.sub.xR/γ.sub.x0 = 1.05,         γ.sub.aR /γ.sub.a0 = 0.45                                    

                                      TABLE 32                                    __________________________________________________________________________    Amount DX (mm) of Movement for Focusing in Direction of Optical Axis at       Telephoto End (116.5 mm) in Third Embodiment                                  __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              .000                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.207                                                                             1)                                                                              .000                                                                             2)                                                                              .224                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.422                                                                             1)                                                                              .000                                                                             2)                                                                              .439                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.721                                                                             1)                                                                              .000                                                                             2)                                                                              .713                                                                              3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.117                                                                            1)                                                                              .000                                                                             2)                                                                              1.039                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.486                                                                            1)                                                                              .000                                                                             2)                                                                              1.926                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.941                                                                            1)                                                                              .000                                                                             2)                                                                              2.612                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.500                                                                            1)                                                                              .000                                                                             2)                                                                              3.457                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________    Imaging Magnification β.sub.K of Lens Units at Telephoto End             (116.5 mm) in Third Embodiment                                                __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              -.490                                                                             3)                                                                              5.579                                                                             4)                                                                              -.500                                        R  10.000                                                                            ANG                                                                              -.207                                                                             1)                                                                              -.009                                                                            2)                                                                              -.473                                                                             3)                                                                              5.579                                                                             4)                                                                              -.500                                        R  5.000                                                                             ANG                                                                              -.422                                                                             1)                                                                              -.018                                                                            2)                                                                              -.456                                                                             3)                                                                              5.579                                                                             4)                                                                              -.500                                        R  3.000                                                                             ANG                                                                              -.721                                                                             1)                                                                              -.031                                                                            2)                                                                              -.436                                                                             3)                                                                              5.579                                                                             4)                                                                              -.500                                        R  2.000                                                                             ANG                                                                              -1.117                                                                            1)                                                                              -.048                                                                            2)                                                                              -.411                                                                             3)                                                                              5.579                                                                             4)                                                                              -.500                                        R  1.000                                                                             ANG                                                                              -2.486                                                                            1)                                                                              -.112                                                                            2)                                                                              -.344                                                                             3)                                                                              5.579                                                                             4)                                                                              -.500                                        R  .700                                                                              ANG                                                                              -3.941                                                                            1)                                                                              -.184                                                                            2)                                                                              -.292                                                                             3)                                                                              5.579                                                                             4)                                                                              -.500                                        R  .500                                                                              ANG                                                                              -6.500                                                                            1)                                                                              -.323                                                                            2)                                                                              -.228                                                                             3)                                                                              5.579                                                                             4)                                                                              -.500                                        __________________________________________________________________________    Conversion Coefficient γ.sub.x Associated With Direction of Optical     Axis at Telephoto End                                                         (116.5 mm) in Third Embodiment                                                __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              5.917                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.207                                                                             1)                                                                              .000                                                                             2)                                                                              6.044                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.422                                                                             1)                                                                              .000                                                                             2)                                                                              6.162                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.721                                                                             1)                                                                              .000                                                                             2)                                                                              6.306                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.117                                                                            1)                                                                              .000                                                                             2)                                                                              6.468                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.486                                                                            1)                                                                              .000                                                                             2)                                                                              6.863                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.941                                                                            1)                                                                              .000                                                                             2)                                                                              7.120                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.500                                                                            1)                                                                              .000                                                                             2)                                                                              7.379                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________    Slope dx/da of Focus Cam at Telephoto End (116.5 mm) in Third                 __________________________________________________________________________    Embodiment                                                                    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              -1.134                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.207                                                                             1)                                                                              .000                                                                             2)                                                                              -1.041                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.422                                                                             1)                                                                              .000                                                                             2)                                                                              -.962                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.721                                                                             1)                                                                              .000                                                                             2)                                                                              -.871                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.117                                                                            1)                                                                              .000                                                                             2)                                                                              -.773                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.486                                                                            1)                                                                              .000                                                                             2)                                                                              -.546                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.941                                                                            1)                                                                              .000                                                                             2)                                                                              -.408                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.500                                                                            1)                                                                              .000                                                                             2)                                                                              -.267                                                                             3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________    Conversion Coefficient γ.sub.a Associated With Direction of             Rotation at                                                                   Telephoto End (116.5 mm) in Third Embodiment                                  __________________________________________________________________________    R  .000                                                                              ANG                                                                              .000                                                                              1)                                                                              .000                                                                             2)                                                                              -6.712                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  10.000                                                                            ANG                                                                              -.207                                                                             1)                                                                              .000                                                                             2)                                                                              -6.291                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  5.000                                                                             ANG                                                                              -.422                                                                             1)                                                                              .000                                                                             2)                                                                              -5.927                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  3.000                                                                             ANG                                                                              -.721                                                                             1)                                                                              .000                                                                             2)                                                                              -5.496                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  2.000                                                                             ANG                                                                              -1.117                                                                            1)                                                                              .000                                                                             2)                                                                              -5.002                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  1.000                                                                             ANG                                                                              -2.486                                                                            1)                                                                              .000                                                                             2)                                                                              -3.748                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  .700                                                                              ANG                                                                              -3.941                                                                            1)                                                                              .000                                                                             2)                                                                              -2.903                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         R  .500                                                                              ANG                                                                              -6.500                                                                            1)                                                                              .000                                                                             2)                                                                              -1.969                                                                            3)                                                                              .000                                                                              4)                                                                              .000                                         __________________________________________________________________________     Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.25,        γ.sub.aR /γ.sub.a0 = 0.29                                    

As can be seen from Tables 30, 31, and 32, at each focal length, theconversion coefficient γ_(x) associated with the direction of theoptical axis increases but the value of the slope (dx/da) of the focuscam decreases as the photographing distance becomes closer to theclosest distance. Therefore, as can be seen from these tables, the valueof the conversion coefficient γ_(a) associated with the direction ofrotation, which is defined as the product of the conversion coefficientγ_(x) and the slope (dx/da) of the focus cam, decreases as thephotographing distance becomes closer to the closest distance by theinfluence of the slope (dx/da) of the focus cam. From Tables 30, 31, and32, the rate of change, from the infinity in-focus position to theclosest in-focus position, of the conversion coefficient γ_(a)associated with the direction of rotation is ×0.50 at the wide-angle end(F=24.7), ×0.45 at the middle position (F=50.0), and ×0.29 at thetelephoto end (F=116.5). When the number N of divisions of the focusrange upon a change in conversion coefficient γ_(a) in the thirdembodiment is calculated using formula (a), and is compared with that inthe embodiment of Japanese Patent Application Laid-Open No. 5-142475,the numbers N_(W), N_(M), and N_(T) of divisions at the wide-angle end,middle position, and telephoto end respectively have the followingvalues:

Embodiment of Japanese Patent Application Laid-Open No. 5-142475

    N.sub.W >9.3 N.sub.M >10.1 N.sub.T >8.1

Third Embodiment

    N.sub.W >3.8 N.sub.M >4.4 N.sub.T >6.7

As described above, in the third embodiment as well, since the rate ofchange of the conversion coefficient γ_(a) associated with the directionof rotation is smaller than that in the conventional system so that thevalues of the numbers N of divisions become small. For this reason, thenumber of data of the conversion coefficient γ_(a) and the correctioncoefficient μ can be reduced, and the storage capacity can besuppressed.

Tables 33, 34, and 35 summarize the calculation results of theconversion coefficient K_(a) and the correction coefficient μ at thewide-angle end (F=24.7), middle position (F=50.0), and telephoto end(F=116.5) according to the third embodiment. The arrangements of thetables and reference symbols are the same as those in the firstembodiment. The position of the focusing lens in the first pair in theupper two tables in each of Tables 33, 34, and 35, i.e., in the thirdand fourth columns is (R, ANGLE)=(0.0, 0.0), and it indicates that thisposition corresponds to the infinity corresponding position. Similarly,the position of the focusing lens in the fourth pair in the lower twotables in each of Tables 33, 34, and 35, i.e., in the ninth and 10thcolumns is (R, ANGLE)=(0.5, -6.5), and it indicates that this positioncorresponds to the closest in-focus (R=0.5 m) corresponding position.

                                      TABLE 33                                    __________________________________________________________________________    Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associated        with Direction                                                                of Rotation and Correction Coefficient μ: (l) at Wide-angle End            (24.7 mm) of Third Embodiment                                                 f = 24.7 mm                                                                   (R,ANGLE) =                                                                          .000                                                                             .000                                                                              10.000                                                                            -.207                                                                             5.000                                                                             -.422                                                                             3.000                                                                             -.721                                       __________________________________________________________________________    POS                                                                              R   r  rs  r   rs  r   rs  r   rs                                          __________________________________________________________________________    1  .000                                                                              -.299                                                                            .000    -.296   -.292   -.286                                       2  10.000 -.297                                                                             -.293                                                                             .000    -.289   -.283                                       3  5.000  -.294   -.290                                                                             -.286                                                                             .000    -.280                                       4  3.000  -.290   -.286   -.282                                                                             -.276                                                                             .000                                        5  2.000  -.285   -.281   -.277   -.271                                       6  1.000  -.268   -.264   -.260   -.255                                       7  .700   -.251   -.247   -.244   -.239                                       8  .500   -.225   -.222   -.219   -.214                                       __________________________________________________________________________    POS                                                                              R   bf l   bf  l   bf  l   bf  l                                           __________________________________________________________________________    1  .000                                                                              .00                                                                              .00 -.06                                                                              7.16                                                                              -.12                                                                              6.15                                                                              -.21                                                                              5.80                                        2  10.000                                                                            .06                                                                              7.84                                                                              .00 .00 -.06                                                                              5.72                                                                              -.15                                                                              5.68                                        3  5.000                                                                             .12                                                                              7.32                                                                              .06 6.35                                                                              .00 .00 -.08                                                                              5.77                                        4  3.000                                                                             .21                                                                              6.76                                                                              .15 6.01                                                                              .08 5.67                                                                              .00 .00                                         5  2.000                                                                             .32                                                                              6.54                                                                              .26 6.02                                                                              .19 5.87                                                                              .11 6.05                                        6  1.000                                                                             .67                                                                              6.30                                                                              .60 6.02                                                                              .54 5.92                                                                              .45 5.85                                        7  .700                                                                              .99                                                                              6.13                                                                              .92 5.91                                                                              .86 5.81                                                                              .77 5.69                                        8  .500                                                                              1.46                                                                             5.92                                                                              1.40                                                                              5.75                                                                              1.33                                                                              5.64                                                                              1.24                                                                              5.51                                        __________________________________________________________________________    (R,ANGLE) =                                                                          2.000                                                                            -1.117                                                                            1.000                                                                             -2.486                                                                            .700                                                                              -3.941                                                                            .500                                                                              -6.500                                      __________________________________________________________________________    POS                                                                              R   r  rs  r   rs  r   rs  r   rs                                          __________________________________________________________________________    1  .000   -.278   -.255   -.234   -.204                                       2  10.000 -.276   -.253   -.232   -.202                                       3  5.000  -.273   -.250   -.229   -.199                                       4  3.000  -.269   -.247   -.226   -.196                                       5  2.000                                                                             -.264                                                                            .000    -.242   -.222   -.193                                       6  1.000  -.248                                                                             -.227                                                                             .000    -.208   -.180                                       7  .700   -.232   -.212                                                                             -.194                                                                             .000    -.168                                       8  .500   -.208   -.190   -.173                                                                             -.150                                                                             .000                                        __________________________________________________________________________    POS                                                                              R   bf l   bf  l   bf  l   bf  l                                           __________________________________________________________________________    1  .000                                                                              -.31                                                                             5.77                                                                              -.63                                                                              5.10                                                                              -.92                                                                              4.47                                                                              -1.32                                                                             3.69                                        2  10.000                                                                            -.25                                                                             5.75                                                                              -.58                                                                              5.08                                                                              -.87                                                                              4.45                                                                              -1.27                                                                             3.68                                        3  5.000                                                                             -.19                                                                             5.81                                                                              -.52                                                                              5.08                                                                              -.81                                                                              4.44                                                                              -1.21                                                                             3.67                                        4  3.000                                                                             -.11                                                                             5.84                                                                              -.44                                                                              5.05                                                                              -.73                                                                              4.42                                                                              -1.14                                                                             3.66                                        5  2.000                                                                             .00                                                                              .00 -.33                                                                              5.01                                                                              -.63                                                                              4.39                                                                              -1.04                                                                             3.64                                        6  1.000                                                                             .34                                                                              5.59                                                                              .00 .00 -.30                                                                              4.32                                                                              -.72                                                                              3.60                                        7  .700                                                                              .66                                                                              5.45                                                                              .31 4.74                                                                              .00 .00 -.43                                                                              3.56                                        8  .500                                                                              1.12                                                                             5.29                                                                              .76 4.66                                                                              .44 4.15                                                                              .00 .00                                         __________________________________________________________________________     Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.75, K.sub.aR     /γ.sub.aR = 1.36                                                   

                                      TABLE 34                                    __________________________________________________________________________    Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associated        with Direction of Rotation and Correction Coefficient μ: (l) at            Middle Position (50.0 mm) of Third Embodiment                                 f = 50.0 mm                                                                   (R,ANGLE) =                                                                          .000                                                                              .000                                                                              10.000                                                                            -.206                                                                             5.000                                                                             -.421                                                                             3.000                                                                             -.720                                      __________________________________________________________________________    POS                                                                              R   r   rs  r   rs  r   rs  r   rs                                         __________________________________________________________________________    1  .000                                                                              -1.235                                                                            .000    -1.209  -1.182  -1.147                                     2  10.000  -1.224                                                                            -1.197                                                                            .000    -1.171  -1.136                                     3  5.000   -1.212  -1.186                                                                            -1.160                                                                            .000    -1.126                                     4  3.000   -1.196  -1.170  -1.145                                                                            -1.111                                                                            .000                                       5  2.000   -1.176  -1.151  -1.125  -1.092                                     6  1.000   -1.112  -1.088  -1.064  -1.033                                     7  .700    -1.049  -1.026  -1.004  -.974                                      8  .500    -.956   -.935   -.914   -.886                                      __________________________________________________________________________    POS                                                                              R   bf  l   bf  l   bf  l   bf  l                                          __________________________________________________________________________    1  .000                                                                              .00 .00 -.25                                                                              26.38                                                                             -.50                                                                              25.72                                                                             -.83                                                                              25.24                                      2  10.000                                                                            .25 29.00                                                                             .00 .00 -.25                                                                              25.32                                                                             -.58                                                                              25.23                                      3  5.000                                                                             .51 28.17                                                                             .25 26.92                                                                             .00 .00 -.34                                                                              25.26                                      4  3.000                                                                             .86 27.81                                                                             .60 26.79                                                                             .34 26.51                                                                             .00 .00                                        5  2.000                                                                             1.31                                                                              27.74                                                                             1.05                                                                              26.90                                                                             .78 26.51                                                                             .43 25.98                                      6  1.000                                                                             2.77                                                                              27.88                                                                             2.49                                                                              27.19                                                                             2.20                                                                              26.71                                                                             1.83                                                                              26.01                                      7  .700                                                                              4.15                                                                              27.62                                                                             3.85                                                                              26.93                                                                             3.55                                                                              26.35                                                                             3.15                                                                              25.52                                      8  .500                                                                              6.21                                                                              27.49                                                                             5.88                                                                              26.82                                                                             5.56                                                                              26.21                                                                             5.12                                                                              25.37                                      __________________________________________________________________________    (R,ANGLE) =                                                                          2.000                                                                             -1.117                                                                            1.000                                                                             -2.491                                                                            .700                                                                              -3.955                                                                            .500                                                                              -6.500                                     __________________________________________________________________________    POS                                                                              R   r   rs  r   rs  r   rs  r   rs                                         __________________________________________________________________________    1  .000    -1.104  -.978   -.873   -.736                                      2  10.000  -1.094  -.969   -.864   -.729                                      3  5.000   -1.083  -.960   -.856   -.722                                      4  3.000   -1.069  -.948   -.845   -.712                                      5  2.000                                                                             -1.052                                                                            .000    -.932   -.830   -.700                                      6  1.000   -.994                                                                             -.879                                                                             .000    -.782   -.659                                      7  .700    -.937   -.827                                                                             -.737                                                                             .000    -.621                                      8  .500    -.852   -.753   -.671                                                                             -.558                                                                             .000                                       POS                                                                              R   bf  l   bf  l   bf  l   bf  l                                          __________________________________________________________________________    1  .000                                                                              -1.23                                                                             24.90                                                                             -2.44                                                                             21.43                                                                             -3.45                                                                             18.78                                                                             -4.78                                                                             15.06                                      2  10.000                                                                            -1.00                                                                             25.03                                                                             -2.22                                                                             21.41                                                                             -3.24                                                                             18.76                                                                             -4.59                                                                             15.03                                      3  5.000                                                                             -.75                                                                              25.24                                                                             -1.99                                                                             21.37                                                                             -3.03                                                                             18.74                                                                             -4.39                                                                             15.00                                      4  3.000                                                                             -.42                                                                              25.72                                                                             -1.68                                                                             21.29                                                                             -2.73                                                                             18.71                                                                             -4.12                                                                             14.96                                      5  2.000                                                                             .00 .00 -1.28                                                                             21.10                                                                             -2.36                                                                             18.66                                                                             -3.77                                                                             14.89                                      6  1.000                                                                             1.37                                                                              24.78                                                                             .00 .00 -1.14                                                                             18.80                                                                             -2.64                                                                             14.64                                      7  .700                                                                              2.66                                                                              24.27                                                                             1.21                                                                              20.71                                                                             .00 .00 -1.58                                                                             14.03                                      8  .500                                                                              4.59                                                                              24.21                                                                             3.02                                                                              21.10                                                                             1.71                                                                              18.99                                                                             .00 .00                                        __________________________________________________________________________     Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.77, K.sub.aR     /γ.sub.aR = 1.32                                                   

                                      TABLE 35                                    __________________________________________________________________________    Conversion Coefficients k.sub.a : (rs), γ.sub.a : (r) Associated        with                                                                          Direction of Rotation and Correction Coefficient μ: (l) at Telephoto       End                                                                           (116.5 mm) of Third Embodiment                                                f = 116.5 mm                                                                  (R,ANGLE) =                                                                          .000                                                                              .000                                                                              10.000                                                                            -.207                                                                             5.000                                                                             -.422                                                                             3.000                                                                             -.721                                      __________________________________________________________________________    POS                                                                              R   r   rs  r   rs  r   rs  r   rs                                         __________________________________________________________________________    1  .000                                                                              -6.715                                                                            .000    -6.320  -5.969  -5.556                                     2  10.000  -6.683                                                                            -6.294                                                                            .000    -5.943  -5.534                                     3  5.000   -6.659  -6.270                                                                            -5.924                                                                            .000    -5.519                                     4  3.000   -6.641  -6.255  -5.911                                                                            -5.489                                                                            .000                                       5  2.000   -6.619  -6.230  -5.882  -5.462                                     6  1.000   -6.540  -6.138  -5.777  -5.346                                     7  .700    -6.438  -6.023  -5.651  -5.210                                     8  .500    -6.234  -5.800  -5.415  -4.962                                     __________________________________________________________________________    POS                                                                              R   bf  l   bf  l   bf  l   bf  l                                          __________________________________________________________________________    1  .000                                                                              .00 .00 -1.31                                                                             307.94                                                                            -2.52                                                                             329.72                                                                            -4.01                                                                             323.62                                     2  10.000                                                                            1.38                                                                              289.98                                                                            .00 .00 -1.28                                                                             394.13                                                                            -2.85                                                                             340.02                                     3  5.000                                                                             2.81                                                                              338.22                                                                            1.35                                                                              365.38                                                                            .00 .00 -1.65                                                                             295.23                                     4  3.000                                                                             4.79                                                                              437.31                                                                            3.22                                                                              523.31                                                                            1.77                                                                              865.92                                                                            .00 .00                                        5  2.000                                                                             7.40                                                                              519.49                                                                            5.68                                                                              565.30                                                                            4.09                                                                              586.44                                                                            2.17                                                                              446.43                                     6  1.000                                                                             16.26                                                                             624.40                                                                            13.99                                                                             565.59                                                                            11.92                                                                             482.70                                                                            9.43                                                                              362.67                                     7  .700                                                                              25.37                                                                             616.08                                                                            22.49                                                                             522.05                                                                            19.89                                                                             432.12                                                                            16.78                                                                             330.17                                     8  .500                                                                              40.52                                                                             566.67                                                                            36.50                                                                             465.13                                                                            32.91                                                                             383.11                                                                            28.68                                                                             299.20                                     __________________________________________________________________________    (R,ANGLE) =                                                                          2.000                                                                             -1.117                                                                            1.000                                                                             -2.486                                                                            .700                                                                              -3.941                                                                            .500                                                                              -6.500                                     __________________________________________________________________________    POS                                                                              R   r   rs  r   rs  r   rs  r   rs                                         __________________________________________________________________________    1  .000    -5.099  -3.999  -3.269  -2.487                                     2  10.000  -5.078  -3.978  -3.249  -2.469                                     3  5.000   -5.060  -3.958  -3.229  -2.450                                     4  3.000   -5.033  -3.928  -3.200  -2.425                                     5  2.000                                                                             -4.996                                                                            .000    -3.890  -3.162  -2.391                                     6  1.000   -4.872                                                                            -3.746                                                                            .000    -3.032  -2.278                                     7  .700    -4.729  -3.609                                                                            -2.903                                                                            .000    -2.164                                     8  .500    -4.475  -3.366  -2.679                                                                            -1.969                                                                            .000                                       __________________________________________________________________________    POS                                                                              R   bf  l   bf  l   bf  l   bf  l                                          __________________________________________________________________________    1  .000                                                                              -5.70                                                                             277.16                                                                            -9.94                                                                             146.83                                                                            -12.89                                                                            101.98                                                                            -16.17                                                                            61.44                                      2  10.000                                                                            -4.63                                                                             284.13                                                                            -9.07                                                                             146.16                                                                            -12.13                                                                            101.70                                                                            -15.54                                                                            61.20                                      3  5.000                                                                             -3.52                                                                             277.88                                                                            -8.17                                                                             144.48                                                                            -11.36                                                                            101.20                                                                            -14.89                                                                            60.91                                      4  3.000                                                                             -2.00                                                                             273.16                                                                            -6.93                                                                             142.16                                                                            -10.30                                                                            100.59                                                                            -14.01                                                                            60.52                                      5  2.000                                                                             .00 .00 -5.32                                                                             138.21                                                                            -8.93                                                                             99.80                                                                             -12.87                                                                            60.01                                      6  1.000                                                                             6.67                                                                              268.04                                                                            .00 .00 -4.41                                                                             98.86                                                                             -9.14                                                                             58.29                                      7  .700                                                                              13.35                                                                             249.19                                                                            5.25                                                                              143.63                                                                            .00 .00 -5.54                                                                             56.02                                      8  .500                                                                              24.09                                                                             231.06                                                                            13.51                                                                             133.32                                                                            6.85                                                                              88.85                                                                             .00 .00                                        __________________________________________________________________________     Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.93, K.sub.aR     /γ.sub.aR = 1.26                                                   

The calculation results of the rate of change of K_(a) with respect toγ_(a) at the infinity in-focus arrangement and the closest in-focusarrangement at the wide-angle end, middle position, and telephoto end inthe embodiment of Japanese Patent Application Laid-Open No. 5-142475 andin the third embodiment of the present invention are as follows.

    ______________________________________                                        Embodiment of Japanese Patent Application Laid-Open No. 5-142475                        Infinity Arrangement                                                                      Closest Arrangement                                               K.sub.aO /γ.sub.aO                                                                  K.sub.aR /γ.sub.aR                                ______________________________________                                        Wide-angle End                                                                            2.75          0.44                                                (F = 36.0)                                                                    Middle Position                                                                           3.36          0.43                                                (F = 50.0)                                                                    Telephoto End                                                                             3.80          0.43                                                (F = 103.0)                                                                   Third Embodiment                                                              Wide-angle End                                                                            0.75          1.36                                                (F = 24.7)                                                                    Middle Position                                                                           0.77          1.32                                                (F = 50.0)                                                                    Telephoto End                                                                             0.93          1.26                                                (F = 116.5)                                                                   ______________________________________                                    

As described above, in the third embodiment as well, since the rate ofchange of K_(a) with respect to γ_(a) is small as compared to theconventional system, the contribution of the correction term (ΔBf/μ) inK_(a) =γ_(a) (1-ΔBf/μ) can be reduced. For this reason, an error of theconversion coefficient Kacalculated based on γ_(a) and μ or an errorfrom the actual lens driving amount Δa obtained when only one pair of aconversion coefficient Δa value and a correction coefficient μ value areset can be reduced.

Next, in the embodiment of Japanese Patent Application Laid-Open No.5-142475 and the third embodiment of the present invention, when thelens driving amounts upon focusing from the infinity in-focus lensarrangement to the closest distance object and upon focusing from theclosest in-focus lens arrangement to the infinity object at thewide-angle end, middle position, and telephoto end are calculated fromΔa=ΔBf/ γ_(a) (1-ΔBf/μ)!, and errors from the actual lens drivingamounts are then calculated, the following values are obtained. Notethat the value of the correction coefficient μ upon focusing from theinfinity in-focus lens arrangement to the closest distance object adoptsa value at the object distance (POS-5), and the value of the correctioncoefficient μ upon focusing from the closest in-focus lens arrangementto the infinity object adopts a value at the object distance (POS-4).

    ______________________________________                                        Embodiment of Japanese Patent Application Laid-Open No. 5-142475                       Infinity Arrangement →                                                              Closest Arrangement →                                     Closest In-focus State                                                                     Infinity In-focus State                                 ______________________________________                                        Wide-angle End                                                                           -4.4%          -13.0%                                              (F = 36.0)                                                                    Middle Position                                                                          -11.8%         -12.0%                                              (F = 50.0)                                                                    Telephoto End                                                                            -12.6%         -14.6%                                              (F = 103.0)                                                                   Third Embodiment                                                              Wide-angle End                                                                           -3.3%          -0.5%                                               (F = 24.7)                                                                    Middle Position                                                                          -0.3%          -0.1%                                               (F = 50.0)                                                                    Telephoto End                                                                            0.7%           -0.3%                                               (F = 116.5)                                                                   ______________________________________                                    

As described above, in the third embodiment as well, even when only apair of a conversion coefficient γ_(a) value and a correctioncoefficient μ value are set for a given lens arrangement range, an errorbetween the conversion coefficient K_(a) calculated from γ_(a) and μ andthe lens driving amount Aa for focusing becomes small as compared to theconventional system, and focusing can be realized with higher accuracy.

Table 36 summarizes the amount (ANGLE DA) of rotation for focusing uponmanual focusing using the focus cam (the middle table in Table 28) ofthe third embodiment, the amount DX (mm) of movement, in the directionof the optical axis:, of the focusing lens unit corresponding to theamount of rotation for focusing, and the displacement amount Bf (mm) ofthe imaging point when the amount (DX) of movement in the direction ofthe optical axis is given.

Note that the arrangement of the table and reference symbols are thesame as those in the first embodiment. The upper table in Table 36summarizes the displacement amount (Bf) of the imaging pointcorresponding to the photographing distances (R=5.0, 3.0, 2.0, 1.0, 0.7,and 0.5 m) in the respective zooming states of the focal lengths(F=24.7, 35.0, 50.0, 70.0, 85.0, and 116.5 mm), and the middle tablesummarizes the values of the amount (ANGLE DA) of rotation for focusingrequired for attaining an optimal in-focus state with respect to therespective photographing distances. The lower table summarizes theamounts (DX) of movement, in the direction of the optical axis, of therespective lens units corresponding to the amount (ANGLE DA) of rotationfor focusing in association with the focal lengths and photographingdistances.

                                      TABLE 36                                    __________________________________________________________________________    Displacement Amount Bf (mm) of Imaging Point and Amount DX                    (mm) of movement for focusing in Third Embodiment                                      0.50 m                                                                             0.70 m                                                                             1.00 m                                                                             2.00 m                                                                             3.00 m                                                                             5.00 m                                      __________________________________________________________________________    F  24.700 Bf                                                                           .000                                                                               .000                                                                               .000                                                                               .000  .000                                                                               .000                                       F  35.000 Bf                                                                           .000                                                                               .003                                                                               .007                                                                               .005  .004                                                                               .002                                       F  50.000 Bf                                                                           .000                                                                               .011                                                                               .005                                                                               .000 -.001                                                                              -.001                                       F  70.000 Bf                                                                           .000                                                                               -.015                                                                              -.022                                                                              -.014                                                                              -.009                                                                              -.006                                       F  85.000 Bf                                                                           .000                                                                               -.022                                                                              -.018                                                                              -.013                                                                              -.009                                                                              -.006                                       F 116.500 Bf                                                                           .000                                                                               .000                                                                               .000                                                                               .000  .000                                                                               .000                                         ANGLE DA                                                                            -6.500                                                                             -3.941                                                                             -2.486                                                                             -1.117                                                                              -.721                                                                              -.422                                       F  24.700 DX                                                                           .000                                                                               .783                                                                               .000                                                                               .000 R                                                                             0.50 m                                           F  35.000 DX                                                                           .000                                                                               1.008                                                                              .000                                                                               .000 R                                                                             0.50 m                                           F  50.000 DX                                                                           .000                                                                               1.366                                                                              .000                                                                               .000 R                                                                             0.50 m                                           F  70.000 DX                                                                           .000                                                                               1.916                                                                              .000                                                                               .000 R                                                                             0.50 m                                           F  85.000 DX                                                                           .000                                                                               2.365                                                                              .000                                                                               .000 R                                                                             0.50 m                                           F 116.500 DX                                                                           .000                                                                               3.457                                                                              .000                                                                               .000 R                                                                             0.50 m                                           F  24.700 DX                                                                           .000                                                                               .539                                                                               .000                                                                               .000 R                                                                             0.70 m                                           F  35.000 DX                                                                           .000                                                                               .698                                                                               .000                                                                               .000 R                                                                             0.70 m                                           F  50.000 DX                                                                           .000                                                                               .956                                                                               .000                                                                               .000 R                                                                             0.70 m                                           F  70.000 DX                                                                           .000                                                                               1.375                                                                              .000                                                                               .000 R                                                                             0.70 m                                           F  85.000 DX                                                                           .000                                                                               1.725                                                                              .000                                                                               .000 R                                                                             0.70 m                                           F 116.500 DX                                                                           .000                                                                               2.612                                                                              .000                                                                               .000 R                                                                             0.70 m                                           F  24.700 DX                                                                           .000                                                                               .368                                                                               .000                                                                               .000 R                                                                             1.00 m                                           F  35.000 DX                                                                           .000                                                                               .476                                                                               .000                                                                               .000 R                                                                             1.00 m                                           F  50.000 DX                                                                           .000                                                                               .662                                                                               .000                                                                               .000 R                                                                             1.00 m                                           F  70.000 DX                                                                           .000                                                                               .969                                                                               .000                                                                               .000 R                                                                             1.00 m                                           F  85.000 DX                                                                           .000                                                                               1.231                                                                              .000                                                                               .000 R                                                                             1.00 m                                           F 116.500 DX                                                                           .000                                                                               1.926                                                                              .000                                                                               .000 R                                                                             1.00 m                                           F  24.700 DX                                                                           .000                                                                               .179                                                                               .000                                                                               .000 R                                                                             2.00 m                                           F  35.000 DX                                                                           .000                                                                               .232                                                                               .000                                                                               .000 R                                                                             2.00 m                                           F  50.000 DX                                                                           .000                                                                               .328                                                                               .000                                                                               .000 R                                                                             2.00 m                                           F  70.000 DX                                                                           .000                                                                               .489                                                                               .000                                                                               .000 R                                                                             2.00 m                                           F  85.000 DX                                                                           .000                                                                               .632                                                                               .000                                                                               .000 R                                                                             2.00 m                                           F 116.500 DX                                                                           .000                                                                               1.039                                                                              .000                                                                               .000 R                                                                             2.00 m                                           F  24.700 DX                                                                           .000                                                                               .118                                                                               .000                                                                               .000 R                                                                             3.00 m                                           F  35.000 DX                                                                           .000                                                                               .153                                                                               .000                                                                               .000 R                                                                             3.00 m                                           F  50.000 DX                                                                           .000                                                                               .218                                                                               .000                                                                               .000 R                                                                             3.00 m                                           F  70.000 DX                                                                           .000                                                                               .327                                                                               .000                                                                               .000 R                                                                             3.00 m                                           F  85.000 DX                                                                           .000                                                                               .426                                                                               .000                                                                               .000 R                                                                             3.00 m                                           F 116.500 DX                                                                           .000                                                                               .713                                                                               .000                                                                               .000 R                                                                             3.00 m                                           F  24.700 DX                                                                           .000                                                                               .070                                                                               .000                                                                               .000 R                                                                             5.00 m                                           F  35.000 DX                                                                           .000                                                                               .092                                                                               .000                                                                               .000 R                                                                             5.00 m                                           F  50.000 DX                                                                           .000                                                                               .131                                                                               .000                                                                               .000 R                                                                             5.00 m                                           F  70.000 DX                                                                           .000                                                                               .197                                                                               .000                                                                               .000 R                                                                             5.00 m                                           F  85.000 DX                                                                           .000                                                                               .258                                                                               .000                                                                               .000 R                                                                             5.00 m                                           F 116.500 DX                                                                           .000                                                                               .439                                                                               .000                                                                               .000 R                                                                             5.00 m                                           __________________________________________________________________________

As can be seen from Table 36, in the zoom lens of the third embodiment,so-called manual focusing can be attained since the displacement amountsof the imaging point at the respective focal lengths and photographingdistances are very small, and fall within the depth of focusindependently of the zooming state and photographing distance.

Fourth Embodiment!

The fourth embodiment is directed to a zoom lens which has a five-unitarrangement, i.e., positive, negative, positive, negative and positivelens units, and attains focusing by a negative second lens unit. In thiszoom lens, the rotation amount ratio (a_(F) /a_(Z)) of the rotationamount for focusing from the infinity in-focus position to the closestin-focus position (R=0.8 m) to the amount of rotation for zooming fromthe wide-angle end (F=28.8) to the telephoto end (F=133.0) is set to be-0.55.

Table 37 below summarizes various paraxial data of an optical system anddata for defining the shape of a focus cam according to the fourthembodiment.

The upper table in Table 37 summarizes the focal lengths and principalpoint interval data of the respective lens units of the optical systemcorresponding to the fourth embodiment in association with six zoomingstates (focal length F=28.8 (1-POS), 35.0 (2-POS), 50.0 (3-POS), 70.0(4-POS), 105.0 (5-POS), and 133.0 mm (6-POS)).

The middle table in Table 37 summarizes spline sample data when theshape of the focus cam in the second lens unit of the fourth embodiment,which is used for focusing, is expressed by the above-mentioned splinefunction associated with the angle a of rotation of a rotatable lensbarrel and the amount x of movement in the direction of the opticalaxis. In this middle table, (1), (2), (3), (4), and (5) correspond tothe first, second, third, fourth, and fifth lens units, respectively.

Furthermore, the lower table in Table 37 summarizes the infinityfocusing positions (infinity corresponding positions) at the respectivefocal lengths (focal length F=28.8, 35.0, 50.0, 70.0, 105.0, and 133.0mm), and the amounts of rotation (amounts of rotation for focusing) uponfocusing to respective photographing distances (R=5.0, 3.0, 2.0, 1.5,1.0, and 0.8 m) using the focus cam of the fourth embodiment. In thistable, since the amount of rotation for zooming from the wide-angle end(F=28.8) to the telephoto end (F=133.0) is set to be 10.0, and theamount of rotation for focusing from the infinity in-focus position tothe closest in-focus position (R=0.8 m) is set to be -5.5, the rotationamount ratio (a_(F) /a_(Z)) of the amount of rotation for focusing tothe amount of rotation for zooming in the fourth embodiment is -0.55.

                                      TABLE 37                                    __________________________________________________________________________    Fourth Embodiment f = 28.8 to 133.0                                           (Rotation Amount Ratio: a.sub.F /a.sub.Z = -0.55)                             Focal lengths and Principal Point Intervals of Lens Units of Fourth           Embodiment                                                                              1-POS                                                                             2-POS                                                                             3-POS                                                                             4-POS                                                                             5-POS                                                                              6-POS                                          __________________________________________________________________________            F 28.8000                                                                           35.0000                                                                           50.0000                                                                           70.0000                                                                           105.0000                                                                           133.0000                                       F1 100.0000                                                                           D1                                                                               9.2812                                                                           14.9225                                                                           24.6593                                                                           33.8704                                                                           45.6942                                                                            51.0696                                        F2 -20.2000                                                                           D2                                                                              34.5121                                                                           30.4389                                                                           24.4402                                                                           20.4110                                                                           16.1765                                                                            13.4016                                        F3  24.1000                                                                           D3                                                                               8.9319                                                                            9.4219                                                                           10.5532                                                                           12.0306                                                                           13.5334                                                                            14.6361                                        F4 -19.6000                                                                           D4                                                                              14.4820                                                                           13.9920                                                                           12.8607                                                                           11.3833                                                                            9.8805                                                                             8.7778                                        F5  31.8000                                                                           D5                                                                              60.1942                                                                           63.5263                                                                           69.6274                                                                           73.5426                                                                           74.9848                                                                            75.1678                                        __________________________________________________________________________    Focus Cam Shape (Spline Interpolation Sample Point)                           Corresponding to Fourth Embodiment                                                  ANGLE                                                                              (1)   (2)  (3)   (4)                                                                              (5)                                            __________________________________________________________________________    1     -10.0000                                                                           .0000 1.8400                                                                             .0000 .0000                                                                            .0000                                          2     -5.5000                                                                            .0000 1.2115                                                                             .0000 .0000                                                                            .0000                                          3     -4.0212                                                                            .0000 .9525                                                                              .0000 .0000                                                                            .0000                                          4     -2.4089                                                                            .0000 .6210                                                                              .0000 .0000                                                                            .0000                                          5     -1.7209                                                                            .0000 .4608                                                                              .0000 .0000                                                                            .0000                                          6     -1.0957                                                                            .0000 .3040                                                                              .0000 .0000                                                                            .0000                                          7     -.6348                                                                             .0000 .1809                                                                              .0000 .0000                                                                            .0000                                          8     .0000                                                                              .0000 .0000                                                                              .0000 .0000                                                                            .0000                                          9     4.5000                                                                             .0000 -1.8003                                                                            .0000 .0000                                                                            .0000                                          10    5.9788                                                                             .0000 -2.7446                                                                            .0000 .0000                                                                            .0000                                          11    7.5911                                                                             .0000 -4.1755                                                                            .0000 .0000                                                                            .0000                                          12    8.2791                                                                             .0000 -5.0009                                                                            .0000 .0000                                                                            .0000                                          13    8.9043                                                                             .0000 -5.9384                                                                            .0000 .0000                                                                            .0000                                          14    9.3652                                                                             .0000 -6.8062                                                                            .0000 .0000                                                                            .0000                                          15    10.0000                                                                            .0000 -8.4464                                                                            .0000 .0000                                                                            .0000                                          16    11.0000                                                                            .0000 -12.6000                                                                           .0000 .0000                                                                            .0000                                          __________________________________________________________________________    Amount of Rotation for Zooming and Amount of Rotation                         for Focusing of Fourth Embodiment                                             (Rotation Amount Ratio: a.sub.F /a.sub.Z = -0.55)                                       Infinity           Amount of                                                  Corresponding                                                                          Photographing                                                                           Rotation for                                     Focal Length                                                                            Position Distance  Focusing                                         __________________________________________________________________________    28.8 mm    .0000    5.00 m    -.635                                           35.0 mm   1.5107    3.00 m   -1.096                                           50.0 mm   4.0821    2.00 m   -1.721                                           70.0 mm   6.3959    1.50 m   -2.409                                           105.0 mm  9.0385    1.00 m   -4.021                                           133.0 mm  10.0000   0.80 m   -5.500                                           Condition Corresponding Value (1)                                                                 1.70                                                      Condition Corresponding Value (2)                                                                 5.49                                                      Condition Corresponding Value (3)                                                                -0.55                                                      Condition Corresponding Value (4)                                                                 0.57 (wide-angle end)                                                         0.29 (telephoto end)                                      Condition Corresponding Value (5)                                                                 0.80 (wide-angle end)                                                         0.87 (telephoto end)                                      Condition Corresponding Value (6)                                                                 1.28 (wide-angle end)                                                         1.25 (telephoto end)                                      __________________________________________________________________________

Table 38 below summarizes the numerical value data of the cams of thefocusing lens unit in the fourth embodiment, which data are calculatedby interpolation based on a spline function on the basis of the sampledata of the focus cam summarized in the middle table in Table 37. Notethat the meanings of the reference symbols in Table 38 are the same asthose in the first embodiment.

                  TABLE 38                                                        ______________________________________                                        Cam Numerical Value Data of                                                   Focusing Lens Unit in Fourth Embodiment                                       Focus Cam         Zoom Compensation Cam                                       Numerical Value Data                                                                            Numerical Value Data                                        ANGLE  (2)       F        ANGLE  (2)   F                                      ______________________________________                                        -5.5000                                                                              1.2115    .0000                                                        -5.0000                                                                              1.1282    .0000                                                        -4.5000                                                                              1.0406    .0000                                                        -4.0000                                                                              .9485     .0000                                                        -3.5000                                                                              .8515     .0000                                                        -3.0000                                                                              .7493     .0000                                                        -2.5000                                                                              .6414     .0000                                                        -2.0000                                                                              .5273     .0000                                                        -1.5000                                                                              .4067     .0000                                                        -1.0000                                                                              .2790     .0000                                                        -.5000 .1436     .0000                                                        .0000  .0000     28.8000  .0000  .0000 28.8000                                .5000  -.1504    30.7227  .5000  -.1838                                                                              30.7227                                1.0000 -.3087    32.7608  1.0000 -.2695                                                                              32.7608                                1.5000 -.4769    34.9510  1.5000 -.2617                                                                              34.9510                                2.0000 -.6569    37.3264  2.0000 -.1633                                                                              37.3264                                2.5000 -.8506    39.9227  2.5000 .0165 39.9227                                3.0000 -1.0599   42.7761  3.0000 .2636 42.7761                                3.5000 -1.2867   45.9227  3.5000 .5598 45.9227                                4.0000 -1.5328   49.3964  4.0000 .8827 49.3964                                4.5000 -1.8003   53.2205  4.5000 1.2098                                                                              53.2205                                5.0000 -2.0913   57.3447  5.0000 1.5309                                                                              57.3447                                5.5000 -2.4098   61.7170  5.5000 1.8374                                                                              61.7170                                6.0000 -2.7601   66.2974  6.0000 2.1167                                                                              66.2974                                6.5000 -3.1477   70.9820  6.5000 2.3572                                                                              70.9820                                7.0000 -3.5832   75.8346  7.0000 2.5476                                                                              75.8346                                7.5000 -4.0780   81.1611  7.5000 2.6738                                                                              81.1611                                8.0000 -4.6449   87.3098  8.0000 2.7311                                                                              87.3098                                8.5000 -5.3068   94.7494  8.5000 2.7193                                                                              94.7494                                9.0000 -6.1040   104.1677 9.0000 2.6370                                                                              104.1677                               9.5000 -7.0980   116.3829 9.5000 2.4925                                                                              116.3829                               10.0000                                                                              -8.4464   133.0000 10.0000                                                                              2.3095                                                                              133.0000                               ______________________________________                                    

The left table in Table 38 summarizes the numerical value data of thefocus cam of the fourth embodiment, and the right table in Table 38summarizes the numerical value data of the zoom compensation cam of thisembodiment. A value obtained by synthesizing the amounts (2) of movementin the direction of the optical axis in the numerical value data of thefocus cam and the zoom compensation cam in the range from the amount ofrotation (ANGLE=0.0) to the amount of rotation (ANGLE=10.0) coincideswith the movement locus of the second lens unit calculated using theparaxial data in the upper table in Table 37.

Tables 39, 40, and 41 below summarize the amount DX (mm) of movement forfocusing, in the direction of the optical axis, of the focusing lensunit, the imaging magnifications β_(k) of the respective lens units, theconversion coefficient γ_(x) associated with the direction of theoptical axis, the slope (dx/da) of the focus cam, and the conversioncoefficient γ_(a) associated with the direction of rotation at thewide-angle end (F=28.8), the middle position (F=70.0), and the telephotoend (F=133.0) according to the fourth embodiment, respectively. Thearrangements of the respective tables and the meanings of the referencesymbols are the same as those in the first embodiment.

                                      TABLE 39                                    __________________________________________________________________________    Amount DX (mm) of Movement for Focusing in Direction of Optical Axis at       Wide-angle End                                                                (28.8 mm) in Fourth Embodiment                                                __________________________________________________________________________    R .000                                                                              ANG .000 1)                                                                            .000 2)                                                                            .000 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 10.000                                                                            ANG -.310 1)                                                                           .000 2)                                                                            .090 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 5.000                                                                             ANG -.635 1)                                                                           .000 2)                                                                            .181 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 3.000                                                                             ANG -1.096 1)                                                                          .000 2)                                                                            .304 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 2.000                                                                             ANG -1.721 1)                                                                          .000 2)                                                                            .461 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 1.500                                                                             ANG -2.409 1)                                                                          .000 2)                                                                            .621 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 1.000                                                                             ANG -4.021 1)                                                                          .000 2)                                                                            .952 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R .800                                                                              ANG -5.500 1)                                                                          .000 2)                                                                            1.212 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       __________________________________________________________________________    Imaging Magnification β.sub.K of Lens Units at Wide-angle End (28.8      mm) in Fourth Embodiment                                                      __________________________________________________________________________    R .000                                                                              ANG .000 1)                                                                            .000 2)                                                                            -.286 3)                                                                           -.662 4)                                                                           -1.701 5)                                                                          -.893                                      R 10.000                                                                            ANG -.310 1)                                                                           -.010 2)                                                                           -.282 3)                                                                           -.662 4)                                                                           -1.701 5)                                                                          -.893                                      R 5.000                                                                             ANG -.635 1)                                                                           -.021 2)                                                                           -.277 3)                                                                           -.662 4)                                                                           -1.701 5)                                                                          -.893                                      R 3.000                                                                             ANG -1.096 1)                                                                          -.036 2)                                                                           -.271 3)                                                                           -.662 4)                                                                           -1.701 5)                                                                          -.893                                      R 2.000                                                                             ANG -1.721 1)                                                                          -.056 2)                                                                           -.264 3)                                                                           -.662 4)                                                                           -1.701 5)                                                                          -.893                                      R 1.500                                                                             ANG -2.409 1)                                                                          -.079 2)                                                                           -.256 3)                                                                           -.662 4)                                                                           -1.701 5)                                                                          -.893                                      R 1.000                                                                             ANG -4.021 1)                                                                          -.129 2)                                                                           -.239 3)                                                                           -.662 4)                                                                           -1.701 5)                                                                          -.893                                      R .800                                                                              ANG -5.500 1)                                                                          -.175 2)                                                                           -.226 3)                                                                           -.662 4)                                                                           -1.701 5)                                                                          -.893                                      __________________________________________________________________________    Conversion Coefficient γ.sub.x Associated With Direction of Optical     Axis at Wide-angle End                                                        (28.8 mm) in Fourth Embodiment                                                __________________________________________________________________________    R .000                                                                              ANG .000 1)                                                                            .000 2)                                                                            .928 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 10.000                                                                            ANG -.310 1)                                                                           .000 2)                                                                            .930 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 5.000                                                                             ANG -.635 1)                                                                           .000 2)                                                                            .933 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 3.000                                                                             ANG -1.096 1)                                                                          .000 2)                                                                            .936 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 2.000                                                                             ANG -1.721 1)                                                                          .000 2)                                                                            .941 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 1.500                                                                             ANG -2.409 1)                                                                          .000 2)                                                                            .945 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 1.000                                                                             ANG -4.021 1)                                                                          .000 2)                                                                            .953 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R .800                                                                              ANG -5.500 1)                                                                          .000 2)                                                                            .959 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       __________________________________________________________________________    Slope dx/da of Focus Cam at Wide-angle End (28.8 mm) in Fourth                __________________________________________________________________________    Embodiment                                                                    R .000                                                                              ANG .000 1)                                                                            .000 2)                                                                            -.294 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 10.000                                                                            ANG -.310 1)                                                                           .000 2)                                                                            -.286 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 5.000                                                                             ANG -.635 1)                                                                           .000 2)                                                                            -.275 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 3.000                                                                             ANG -1.096 1)                                                                          .000 2)                                                                            -.260 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 2.000                                                                             ANG -1.721 1)                                                                          .000 2)                                                                            -.242 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 1.500                                                                             ANG -2.409 1)                                                                          .000 2)                                                                            -.224 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 1.000                                                                             ANG -4.021 1)                                                                          .000 2)                                                                            -.189 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R .800                                                                              ANG -5.500 1)                                                                          .000 2)                                                                            -.163 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       __________________________________________________________________________    Conversion Coefficient γ.sub.a Associated With Direction of             Rotation at Wide-angle End                                                    (28.8 mm) in Fourth Embodiment                                                __________________________________________________________________________    R .000                                                                              ANG .000 1)                                                                            .000 2)                                                                            -.273 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 10.000                                                                            ANG -.310 1)                                                                           .000 2)                                                                            -.266 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 5.000                                                                             ANG -.635 1)                                                                           .000 2)                                                                            -.256 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 3.000                                                                             ANG -1.096 1)                                                                          .000 2)                                                                            -.243 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 2.000                                                                             ANG -1.721 1)                                                                          .000 2)                                                                            -.228 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 1.500                                                                             ANG -2.409 1)                                                                          .000 2)                                                                            -.212 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 1.000                                                                             ANG -4.021 1)                                                                          .000 2)                                                                            -.180 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R .800                                                                              ANG -5.500 1)                                                                          .000 2)                                                                            -.156 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       __________________________________________________________________________     Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.03,        γ.sub.aR /γ.sub.a0 = 0.57                                    

                                      TABLE 40                                    __________________________________________________________________________    Amount DX (mm) of Movement for Focusing in Direction of Optical Axis at       Middle Position                                                               (70.0 mm) in Fourth Embodiment                                                __________________________________________________________________________    R .000                                                                              ANG .000 1)                                                                            .000 2)                                                                            .000 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 10.000                                                                            ANG -.308 1)                                                                           .000 2)                                                                            .238 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 5.000                                                                             ANG -.631 1)                                                                           .000 2)                                                                            .472 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 3.000                                                                             ANG -1.088 1)                                                                          .000 2)                                                                            .779 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                       R 2.000                                                                             ANG -1.708 1)                                                                          .000 2)                                                                            1.157 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 1.500                                                                             ANG -2.389 1)                                                                          .000 2)                                                                            1.527 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 1.000                                                                             ANG -3.997 1)                                                                          .000 2)                                                                            2.253 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R .800                                                                              ANG -5.500 1)                                                                          .000 2)                                                                            2.789 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       __________________________________________________________________________    Imaging Magnification β.sub.K of Lens Units at Middle Position (70.0     mm) in Fourth Embodiment                                                      __________________________________________________________________________    R .000                                                                              ANG .000 1)                                                                            .000 2)                                                                            -.440 3)                                                                           -.949 4)                                                                           -1.278 5)                                                                          -1.313                                     R 10.000                                                                            ANG -.308 1)                                                                           -.010 2)                                                                           -.428 3)                                                                           -.949 4)                                                                           -1.278 5)                                                                          -1.313                                     R 5.000                                                                             ANG -.631 1)                                                                           -.021 2)                                                                           -.416 3)                                                                           -.949 4)                                                                           -1.278 5)                                                                          -1.313                                     R 3.000                                                                             ANG -1.088 1)                                                                          -.036 2)                                                                           -.401 3)                                                                           -.949 4)                                                                           -1.278 5)                                                                          -1.313                                     R 2.000                                                                             ANG -1.708 1)                                                                          -.057 2)                                                                           -.383 3)                                                                           -.949 4)                                                                           -1.278 5)                                                                          -1.313                                     R 1.500                                                                             ANG -2.389 1)                                                                          -.080 2)                                                                           -.364 3)                                                                           -.949 4)                                                                           -1.278 5)                                                                          -1.313                                     R 1.000                                                                             ANG -3.997 1)                                                                          -.134 2)                                                                           -.328 3)                                                                           -.949 4)                                                                           -1.278 5)                                                                          -1.313                                     R .800                                                                              ANG -5.500 1)                                                                          -.182 2)                                                                           -.302 3)                                                                           -.949 4)                                                                           -1.278 5)                                                                          -1.313                                     __________________________________________________________________________    Conversion Coefficient γ.sub.x Associated With Direction of Optical     Axis at Middle Position                                                       (70.0 mm) in Fourth Embodiment                                                __________________________________________________________________________    R .000                                                                              ANG .000 1)                                                                            .000 2)                                                                            2.043 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 10.000                                                                            ANG -.308 1)                                                                           .000 2)                                                                            2.069 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 5.000                                                                             ANG -.631 1)                                                                           .000 2)                                                                            2.094 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 3.000                                                                             ANG -1.088 1)                                                                          .000 2)                                                                            2.125 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 2.000                                                                             ANG -1.708 1)                                                                          .000 2)                                                                            2.163 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 1.500                                                                             ANG -2.389 1)                                                                          .000 2)                                                                            2.197 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 1.000                                                                             ANG -3.997 1)                                                                          .000 2)                                                                            2.260 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R .800                                                                              ANG -5.500 1)                                                                          .000 2)                                                                            2.303 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       __________________________________________________________________________    Slope dx/da of Focus Cam at Middle Position (70.0 mm) in Fourth               __________________________________________________________________________    Embodiment                                                                    R .000                                                                              ANG .000 1)                                                                            .000 2)                                                                            -.800 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 10.000                                                                            ANG -.308 1)                                                                           .000 2)                                                                            -.748 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 5.000                                                                             ANG -.631 1)                                                                           .000 2)                                                                            -.702 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 3.000                                                                             ANG -1.088 1)                                                                          .000 2)                                                                            -.644 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 2.000                                                                             ANG -1.708 1)                                                                          .000 2)                                                                            -.576 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 1.500                                                                             ANG -2.389 1)                                                                          .000 2)                                                                            -.514 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R 1.000                                                                             ANG -3.997 1)                                                                          .000 2)                                                                            -.396 3)                                                                           .000 4)                                                                            .000 5)                                                                            .090                                       R .800                                                                              ANG -5.500 1)                                                                          .000 2)                                                                            -.322 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       __________________________________________________________________________    Conversion Coefficient γ.sub.a Associated With Direction of             Rotation at Middle Position                                                   (70.0 mm) in Fourth Embodiment                                                __________________________________________________________________________    R .000                                                                              ANG .000 1)                                                                            .000 2)                                                                            -1.634 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                       R 10.000                                                                            ANG -.308 1)                                                                           .000 2)                                                                            -1.548 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                       R 5.000                                                                             ANG -.631 1)                                                                           .000 2)                                                                            -1.470 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                       R 3.000                                                                             ANG -1.088 1)                                                                          .000 2)                                                                            -1.368 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                       R 2.000                                                                             ANG -1.708 1)                                                                          .000 2)                                                                            -1.245 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                       R 1.500                                                                             ANG -2.389 1)                                                                          .000 2)                                                                            -1.128 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                       R 1.000                                                                             ANG -3.997 1)                                                                          .000 2)                                                                            -.895 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       R .800                                                                              ANG -5.500 1)                                                                          .000 2)                                                                            -.741 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                       __________________________________________________________________________     Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.13,        γ.sub.aR /γ.sub.a0 = 0.45                                    

                                      TABLE 41                                    __________________________________________________________________________    Amount DX (mm) of Movement for Focusing in Direction of Optical Axis at       Telephoto                                                                     End (133.0 mm) in Fourth Embodiment                                           __________________________________________________________________________    R .000                                                                              ANG                                                                              .000 1)                                                                            .000 2)                                                                            .000 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                        R 10.000                                                                            ANG                                                                              -.307 1)                                                                           .000 2)                                                                            .887 3)                                                                            .000 4)                                                                            .000 5)                                                                            .000                                        R 5.000                                                                             ANG                                                                              -.635 1)                                                                           .000 2)                                                                            1.640 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        R 3.000                                                                             ANG                                                                              -1.096 1)                                                                          .000 2)                                                                            2.508 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        R 2.000                                                                             ANG                                                                              -1.721 1)                                                                          .000 2)                                                                            3.446 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        R 1.500                                                                             ANG                                                                              -2.409 1)                                                                          .000 2)                                                                            4.271 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        R 1.000                                                                             ANG                                                                              -4.021 1)                                                                          .000 2)                                                                            5.702 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        R .800                                                                              ANG                                                                              -5.500 1)                                                                          .000 2)                                                                            6.646 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        __________________________________________________________________________    Imaging Magnification β.sub.K of Lens Units at Telephoto End (133.0      mm) in Fourth Embodiment                                                      __________________________________________________________________________    R .000                                                                              ANG                                                                              .000 1)                                                                            .000 2)                                                                            -.703 3)                                                                           -1.017 4)                                                                          -1.364 5)                                                                          -1.364                                      R 10.000                                                                            ANG                                                                              -.307 1)                                                                           -.010 2)                                                                           -.659 3)                                                                           -1.017 4)                                                                          -1.364 5)                                                                          -1.364                                      R 5.000                                                                             ANG                                                                              -.635 1)                                                                           -.021 2)                                                                           -.622 3)                                                                           -1.017 4)                                                                          -1.364 5)                                                                          -1.364                                      R 3.000                                                                             ANG                                                                              -1.096 1)                                                                          -.037 2)                                                                           -.579 3)                                                                           -1.017 4)                                                                          -1.364 5)                                                                          -1.364                                      R 2.000                                                                             ANG                                                                              -1.721 1)                                                                          -.058 2)                                                                           -.533 3)                                                                           -1.017 4)                                                                          -1.364 5)                                                                          -1.364                                      R 1.500                                                                             ANG                                                                              -2,409 1)                                                                          -.081 2)                                                                           -.492 3)                                                                           -1.017 4)                                                                          -1.364 5)                                                                          -1.364                                      R 1.000                                                                             ANG                                                                              -4.021 1)                                                                          -.136 2)                                                                           -.421 3)                                                                           -1.017 4)                                                                          -1.364 5)                                                                          -1.364                                      R .800                                                                              ANG                                                                              -5.500 1)                                                                          -.186 2)                                                                           -.374 3)                                                                           -1.017 4)                                                                          -1.364 5)                                                                          -1.364                                      __________________________________________________________________________    Conversion Coefficient γ.sub.x Associated With Direction of Optical     Axis at Telephoto End                                                         (133.0 mm) in Fourth Embodiment                                               __________________________________________________________________________    R .000                                                                              ANG                                                                              .000 1)                                                                            .000 2)                                                                            1.809 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        R 10.000                                                                            ANG                                                                              -.307 1)                                                                           .000 2)                                                                            2.024 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        R 5.000                                                                             ANG                                                                              -.635 1)                                                                           .000 2)                                                                            2.194 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        R 3.000                                                                             ANG                                                                              -1.096 1)                                                                          .000 2)                                                                            2.379 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        R 2.000                                                                             ANG                                                                              -1.721 1)                                                                          .000 2)                                                                            2.564 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        R 1.500                                                                             ANG                                                                              -2.409 1)                                                                          .000 2)                                                                            2.713 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        R 1.000                                                                             ANG                                                                              -4.021 1)                                                                          .000 2)                                                                            2.945 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        R .800                                                                              ANG                                                                              -5.500 1)                                                                          .000 2)                                                                            3.078 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        __________________________________________________________________________    Slope dx/da of Focus Cam at Telephoto End (133.0 mm) in Fourth                __________________________________________________________________________    Embodiment                                                                    R .000                                                                              ANG                                                                              .000 1)                                                                            .000 2)                                                                            -3.257 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                        R 10.000                                                                            ANG                                                                              -.307 1)                                                                           .000 2)                                                                            -2.558 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                        R 5.000                                                                             ANG                                                                              -.635 1)                                                                           .000 2)                                                                            -2.090 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                        R 3.000                                                                             ANG                                                                              -1.096 1)                                                                          .000 2)                                                                            -1.696 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                        R 2.000                                                                             ANG                                                                              -1.721 1)                                                                          .000 2)                                                                            -1.333 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                        R 1.500                                                                             ANG                                                                              -2.409 1)                                                                          .000 2)                                                                            -1.083 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                        R 1.000                                                                             ANG                                                                              -4.021 1)                                                                          .000 2)                                                                            -.732 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        R .800                                                                              ANG                                                                              -5.500 1)                                                                          .000 2)                                                                            -.557 3)                                                                           .000 4)                                                                            .000 5)                                                                            .000                                        __________________________________________________________________________    Conversion Coefficient γ.sub.a Associated With Direction of             Rotation at Telephoto End                                                     (133.0 mm) in Fourth Embodiment                                               __________________________________________________________________________    R .000                                                                              ANG                                                                              .000 1)                                                                            .000 2)                                                                            -5.894 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                        R 10.000                                                                            ANG                                                                              -.307 1)                                                                           .000 2)                                                                            -5.175 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                        R 5.000                                                                             ANG                                                                              -.635 1)                                                                           .000 2)                                                                            -4.587 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                        R 3.000                                                                             ANG                                                                              -1.096 1)                                                                          .000 2)                                                                            -4.034 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                        R 2.000                                                                             ANG                                                                              -1.721 1)                                                                          .000 2)                                                                            -3.418 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                        R 1.500                                                                             ANG                                                                              -2.409 1)                                                                          .000 2)                                                                            -2.938 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                        R 1.000                                                                             ANG                                                                              -4.021 1)                                                                          .000 2)                                                                            -2.156 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                        R .800                                                                              ANG                                                                              -5.500 1)                                                                          .000 2)                                                                            -1.716 3)                                                                          .000 4)                                                                            .000 5)                                                                            .000                                        __________________________________________________________________________     Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.70,        γ.sub.aR /γ.sub.a0 = 0.29                                    

As can be seen from Tables 39, 40, and 41, at each focal length, theconversion coefficient γ_(x) associated with the direction of theoptical axis increases but the value of the slope (dx/da) of the focuscam decreases as the photographing distance becomes closer to theclosest distance. Therefore, as can be seen from these tables, the valueof the conversion coefficient γ_(a) associated with the direction ofrotation, which is defined as the product of the conversion coefficientγ_(x) and the slope (dx/da) of the focus cam, decreases as thephotographing distance becomes closer to the closest distance by theinfluence of the slope (dx/da) of the focus cam. From Tables 39, 40, and41, the rate of change, from the infinity in-focus position to theclosest in-focus position, of the conversion coefficient γ_(a)associated with the direction of rotation is ×0.57 at the wide-angle end(F=28.8), ×0.45 at the middle position (F=70.0), and ×0.29 at thetelephoto end (F=133.0). When the number N of divisions of the focusrange upon a change in conversion coefficient γ_(a) in the fourthembodiment is calculated using formula (a), and is compared with that inthe embodiment of Japanese Patent Application Laid-Open No. 5-142475,the numbers N_(W), N_(M), and N_(T) of divisions at the wide-angle end,middle position, and telephoto end respectively have the followingvalues:

Embodiment of Japanese Patent Application Laid-Open No. 5-142475

    N.sub.W >9..3 N.sub.M >10.1 N.sub.T >8.1

Fourth Embodiment

    N.sub.W >3.1 N.sub.M >4.3 N.sub.T >6.8

Therefore, as can be seen from the above comparison, although the ratio(Δx_(TR) /Δx_(WR)) between the amounts ΔX_(TR) and ΔX_(WR) of movement,in the direction of the optical axis, of the focusing lens unit requiredfor focusing from the infinity position to the closest distance positionat the wide-angle end and the telephoto end in the first embodiment islarger than that in the embodiment of Japanese Patent ApplicationLaid-Open No. 5-142475 (the embodiment of Japanese Patent ApplicationLaid-Open No. 5-142475: 3.94; the fourth embodiment: 5.49), the valuesof the numbers N of divisions become small conversely.

As described above, in the fourth embodiment as well, since the rate ofchange of the conversion coefficient γ_(a) associated with the directionof rotation is smaller than that in the conventional system so that thevalues of the numbers N of divisions become small. For this reason, thenumber of data of the conversion coefficient γ_(a) and the correctioncoefficient μ can be reduced, and the storage capacity can besuppressed.

Tables 42, 43, and 44 summarize the calculation results of theconversion coefficient K_(a) and the correction coefficient μ at thewide-angle end (F=28.8), middle position (F=70.0), and telephoto end(F=133.0) according to the fourth embodiment. The arrangements of thetables and reference symbols are the same as those in the firstembodiment. The position of the focusing lens in the first pair in theupper two tables in each of Tables 42, 43, and 44, i.e., in the thirdand fourth columns is (R, ANGLE)=(0.0, 0.0), and it indicates that thisposition corresponds to the infinity corresponding position. Similarly,the position of the focusing lens in the fourth pair in the lower twotables in each of Tables 42, 43, and 44, i.e., in the ninth and tenthcolumns is (R, ANGLE)=(0.8, -5.5), and it indicates that this positioncorresponds to the closest in-focus (R=0.8 m) corresponding position.

                                      TABLE 42                                    __________________________________________________________________________    Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associated        with Direction                                                                of Rotation and Correction Coefficient μ: (l) at Wide-angle End (28.8      mm)                                                                           of Fourth Embodiment                                                          f = 28.8 mm                                                                   (R,ANGLE) =                                                                          .000                                                                              .000                                                                              10.000                                                                            -.310                                                                             5.000                                                                             -.635                                                                             3.000                                                                             -1.096                                     __________________________________________________________________________    POS                                                                              R   r   rs  r   rs  r   rs  r   rs                                         __________________________________________________________________________    1  .000                                                                              -.273                                                                             .000    -.268   -.263   -.256                                      2  10.000  -.270                                                                             -.266                                                                             .000    -.260   -.252                                      3  5.000   -.267   -.262                                                                             -.256                                                                             .000    -.249                                      4  3.000   -.262   -.256   -.251                                                                             -.243                                                                             .000                                       5  2.000   -.255   -.249   -.244   -.237                                      6  1.500   -.247   -.242   -.237   -.230                                      7  1.000   -.231   -.226   -.221   -.214                                      8  .800    -.217   -.213   -.208   -.202                                      __________________________________________________________________________    POS                                                                              R   bf  l   bf  l   bf  l   bf  l                                          __________________________________________________________________________    1  .000                                                                              .00 .00 -.08                                                                              7.88                                                                              -.17                                                                              6.13                                                                              -.28                                                                              5.48                                       2  10.000                                                                            .08 9.08                                                                              .00 .00 -.08                                                                              5.57                                                                              -.20                                                                              5.31                                       3  5.000                                                                             .17 7.94                                                                              .09 6.32                                                                              .00 .00 -.11                                                                              5.39                                       4  3.000                                                                             .29 6.96                                                                              .20 5.80                                                                              .12 5.22                                                                              .00 .00                                        5  2.000                                                                             .44 6.52                                                                              .35 5.73                                                                              .26 5.43                                                                              .15 5.45                                       6  1.500                                                                             .60 6.30                                                                              .51 5.70                                                                              .42 5.46                                                                              .30 5.39                                       7  1.000                                                                             .93 6.02                                                                              .84 5.61                                                                              .75 5.42                                                                              .63 5.28                                       8  .800                                                                              1.20                                                                              5.88                                                                              1.10                                                                              5.55                                                                              1.01                                                                              5.37                                                                              .89 5.21                                       __________________________________________________________________________    (R,ANGLE) =                                                                          2.000                                                                             -1.721                                                                            1.500                                                                             -2.409                                                                            1.000                                                                             -4.021                                                                            .800                                                                              -5.500                                     __________________________________________________________________________    POS                                                                              R   r   rs  r   rs  r   rs  r   rs                                         __________________________________________________________________________    1  .000    -.246   -.236   -.215   -.199                                      2  10.000  -.243   -.233   -.212   -.196                                      3  5.000   -.239   -.229   -.209   -.193                                      4  3.000   -.234   -.224   -.205   -.189                                      5  2.000                                                                             -.228                                                                             .000    -.218   -.199   -.184                                      6  1.500   -.221                                                                             -.212                                                                             .000    -.193   -.178                                      7  1.000   -.206   -.197                                                                             -.180                                                                             .000    -.166                                      8  .800    -.194   -.186   -.169                                                                             -.156                                                                             .000                                       __________________________________________________________________________    POS                                                                              R   bf  l   bf  l   bf  l   bf  l                                          __________________________________________________________________________    1  .000                                                                              -.42                                                                              5.25                                                                              -.57                                                                              4.93                                                                              -.87                                                                              4.37                                                                              -1.10                                                                             3.97                                       2  10.000                                                                            -.34                                                                              5.19                                                                              -.49                                                                              4.89                                                                              -.79                                                                              4.35                                                                              -1.02                                                                             3.96                                       3  5.000                                                                             -.26                                                                              5.22                                                                              -.41                                                                              4.89                                                                              -.71                                                                              4.34                                                                              -.94                                                                              3.95                                       4  3.000                                                                             -.15                                                                              5.22                                                                              -.29                                                                              4.85                                                                              -.60                                                                              4.32                                                                              -.83                                                                              3.94                                       5  2.000                                                                             .00 .00 -.15                                                                              4.79                                                                              -.46                                                                              4.29                                                                              -.69                                                                              3.92                                       6  1.500                                                                             .15 5.04                                                                              .00 .00 -.31                                                                              4.27                                                                              -.55                                                                              3.91                                       7  1.000                                                                             .47 4.98                                                                              .32 4.73                                                                              .00 .00 -.25                                                                              3.89                                       8  .800                                                                              .73 4.94                                                                              .57 4.69                                                                              .25 4.20                                                                              .00 .00                                        __________________________________________________________________________     Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.80, K.sub.aR     /γ.sub.aR = 1.28                                                   

                                      TABLE 43                                    __________________________________________________________________________    Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associated        with Direction                                                                of Rotation and Correction Coefficient μ: (l) at Middle Position (70.0     mm)                                                                           of Fourth Embodiment                                                          f = 70.0 mm                                                                   (R,ANGLE) =                                                                          .000                                                                              .000                                                                              10.000                                                                            -.308                                                                             5.000                                                                             -.631                                                                             3.000                                                                             -1.088                                     __________________________________________________________________________    POS                                                                              R   r   rs  r   rs  r   rs  r   rs                                         __________________________________________________________________________    1  .000                                                                              -1.634                                                                            .000    -1.570  -1.509  -1.432                                     2  10.000  -1.611                                                                            -1.549                                                                            .000    -1.490  -1.414                                     3  5.000   -1.590  -1.528                                                                            -1.471                                                                            .000    -1.395                                     4  3.000   -1.560  -1.500  -1.443                                                                            -1.367                                                                            .000                                       5  2.000   -1.521  -1.462  -1.405  -1.332                                     6  1.500   -1.479  -1.421  -1.366  -1.295                                     7  1.000   -1.383  -1.328  -1.275  -1.207                                     8  .800    -1.298  -1.246  -1.195  -1.130                                     __________________________________________________________________________    POS                                                                              R   bf  l   bf  l   bf  l   bf  l                                          __________________________________________________________________________    1  .000                                                                              .00 .00 -.48                                                                              36.20                                                                             -.95                                                                              36.95                                                                             -1.56                                                                             32.72                                      2  10.000                                                                            .50 35.47                                                                             .00 .00 -.48                                                                              38.75                                                                             -1.10                                                                             32.41                                      3  5.000                                                                             1.00                                                                              36.85                                                                             .49 37.16                                                                             .00 .00 -.64                                                                              31.51                                      4  3.000                                                                             1.70                                                                              37.59                                                                             1.17                                                                              37.20                                                                             .66 33.78                                                                             .00 .00                                        5  2.000                                                                             2.60                                                                              37.47                                                                             2.05                                                                              36.41                                                                             1.51                                                                              33.65                                                                             .83 31.88                                      6  1.500                                                                             3.53                                                                              37.24                                                                             2.96                                                                              35.94                                                                             2.40                                                                              33.53                                                                             1.68                                                                              31.66                                      7  1.000                                                                             5.53                                                                              35.93                                                                             4.90                                                                              34.34                                                                             4.29                                                                              32.18                                                                             3.51                                                                              29.98                                      8  .800                                                                              7.14                                                                              34.68                                                                             6.47                                                                              33.01                                                                             5.82                                                                              31.10                                                                             4.99                                                                              28.77                                      __________________________________________________________________________    (R,ANGLE) =                                                                          2.000                                                                             -1.708                                                                            1.500                                                                             -2.389                                                                            1.000                                                                             -3.997                                                                            .800                                                                              -5.500                                     __________________________________________________________________________    POS                                                                              R   r   rs  r   rs  r   rs  r   rs                                         __________________________________________________________________________    1  .000    -1.340  -1.252  -1.082  -.960                                      2  10.000  -1.322  -1.235  -1.067  -.946                                      3  5.000   -1.304  -1.218  -1.052  -.931                                      4  3.000   -1.278  -1.194  -1.030  -.911                                      5  2.000                                                                             -1.244                                                                            .000    -1.162  -1.001  -.884                                      6  1.500   -1.210                                                                            -1.128                                                                            .000    -.969   -.855                                      7  1.000   -1.126  -1.047                                                                            -.896                                                                             .000    -.790                                      8  .800    -1.053  -.978   -.836                                                                             -.741                                                                             .000                                       __________________________________________________________________________    POS                                                                              R   bf  l   bf  l   bf  l   bf  l                                          __________________________________________________________________________    1  .000                                                                              -2.29                                                                             29.65                                                                             -2.99                                                                             27.18                                                                             -4.33                                                                             20.73                                                                             -5.28                                                                             17.90                                      2  10.000                                                                            -1.85                                                                             29.41                                                                             -2.57                                                                             27.01                                                                             -3.94                                                                             20.53                                                                             -4.91                                                                             17.79                                      3  5.000                                                                             -1.40                                                                             29.06                                                                             -2.14                                                                             26.80                                                                             -3.54                                                                             20.32                                                                             -4.53                                                                             17.68                                      4  3.000                                                                             -.79                                                                              28.69                                                                             -1.55                                                                             26.58                                                                             -3.00                                                                             20.00                                                                             -4.02                                                                             17.54                                      5  2.000                                                                             .00 .00 -.79                                                                              25.93                                                                             -2.29                                                                             19.53                                                                             -3.35                                                                             17.37                                      6  1.500                                                                             .82 29.92                                                                             .00 .00 -1.56                                                                             19.04                                                                             -2.66                                                                             17.29                                      7  1.000                                                                             2.58                                                                              27.13                                                                             1.68                                                                              23.57                                                                             .00 .00 -1.19                                                                             17.93                                      8  .800                                                                              3.99                                                                              25.98                                                                             3.04                                                                              22.93                                                                             1.26                                                                              18.95                                                                             .00 .00                                        __________________________________________________________________________     Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.79, K.sub.aR     /γ.sub.aR = 1.30                                                   

                                      TABLE 44                                    __________________________________________________________________________    Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r)                   Associated with Direction of Rotation and Correction                          Coefficient μ: (l) at Telephoto End                                        (133.0 mm) of Fourth Embodiment                                               f = 133.0 mm                                                                  (R,ANGLE) =                                                                          .000                                                                              .000                                                                              10.000                                                                            -.307                                                                             5.000                                                                             -.635                                                                             3.000                                                                             -1.096                                     __________________________________________________________________________    POS                                                                              R   r   rs  r   rs  r   rs  r   rs                                         __________________________________________________________________________    1  .000                                                                              -5.886                                                                            .000    -5.248  -4.706  -4.166                                     2  10.000  -5.859                                                                            -5.168                                                                            .000    -4.633  -4.114                                     3  5.000   -5.776  -5.094                                                                            -4.589                                                                            .000    -4.083                                     4  3.000   -5.716  -5.052  -4.559                                                                            -4.030                                                                            .000                                       5  2.000   -5.635  -4.975  -4.476  -3.944                                     6  1.500   -5.545  -4.887  -4.387  -3.859                                     7  1.000   -5.337  -4.681  -4.185  -3.666                                     8  .800    -5.152  -4.500  -4.009  -3.501                                     __________________________________________________________________________    POS                                                                              R   bf  l   bf  l   bf  l   bf  l                                          __________________________________________________________________________    1  .000                                                                              .00 .00 -1.61                                                                             104.68                                                                            -2.99                                                                             117.43                                                                            -4.57                                                                             135.10                                     2  10.000                                                                            1.80                                                                              390.80                                                                            .00 .00 -1.52                                                                             156.12                                                                            -3.24                                                                             155.10                                     3  5.000                                                                             3.67                                                                              196.37                                                                            1.67                                                                              115.70                                                                            .00 .00 -1.88                                                                             142.85                                     4  3.000                                                                             6.26                                                                              217.09                                                                            3.98                                                                              176.51                                                                            2.10                                                                              321.92                                                                            .00 .00                                        5  2.000                                                                             9.70                                                                              227.03                                                                            7.03                                                                              187.57                                                                            4.86                                                                              198.58                                                                            2.47                                                                              115.54                                     6  1.500                                                                             13.36                                                                             230.65                                                                            10.27                                                                             188.36                                                                            7.78                                                                              177.34                                                                            5.07                                                                              119.12                                     7  1.000                                                                             21.46                                                                             230.00                                                                            17.38                                                                             184.30                                                                            14.17                                                                             160.89                                                                            10.72                                                                             118.62                                     8  .800                                                                              28.34                                                                             227.20                                                                            23.37                                                                             180.68                                                                            19.51                                                                             154.48                                                                            15.42                                                                             117.40                                     __________________________________________________________________________    (R,ANGLE) =                                                                          2.000                                                                             -1.721                                                                            1.500                                                                             -2.409                                                                            1.000                                                                             -4.021                                                                            .800                                                                              -5.500                                     __________________________________________________________________________    POS                                                                              R   r   rs  r   rs  r   rs  r   rs                                         __________________________________________________________________________    1  .000    -3.633  -3.203  -2.533  -2.139                                     2  10.000  -3.589  -3.163  -2.500  -2.110                                     3  5.000   -3.554  -3.129  -2.469  -2.082                                     4  3.000   -3.498  -3.076  -2.424  -2.042                                     5  2.000                                                                             -3.418                                                                            .000    -3.007  -2.364  -1.990                                     6  1.500   -3.344                                                                            -2.938                                                                            .000    -2.301  -1.934                                     7  1.000   -3.164  -2.767                                                                            -2.155                                                                            .000    -1.813                                     8  .800    -3.013  -2.628  -2.047                                                                            -1.716                                                                            .000                                       __________________________________________________________________________    POS                                                                              R   bf  l   bf  l   bf  l   bf  l                                          __________________________________________________________________________    1  .000                                                                              -6.25                                                                             99.38                                                                             -7.72                                                                             85.58                                                                             -10.19                                                                            57.95                                                                             -11.77                                                                            47.75                                      2  10.000                                                                            -5.07                                                                             101.47                                                                            -6.65                                                                             86.68                                                                             -9.29                                                                             57.86                                                                             -10.96                                                                            47.73                                      3  5.000                                                                             -3.86                                                                             96.93                                                                             -5.55                                                                             85.46                                                                             -8.36                                                                             57.26                                                                             -10.13                                                                            47.49                                      4  3.000                                                                             -2.19                                                                             93.61                                                                             -4.04                                                                             85.84                                                                             -7.09                                                                             56.72                                                                             -9.00                                                                             47.34                                      5  2.000                                                                             .00 .00 -2.07                                                                             88.39                                                                             -5.44                                                                             55.88                                                                             -7.52                                                                             47.17                                      6  1.500                                                                             2.30                                                                              105.20                                                                            .00 .00 -3.71                                                                             54.68                                                                             -5.98                                                                             47.08                                      7  1.000                                                                             7.28                                                                              97.94                                                                             4.46                                                                              76.49                                                                             .00 .00 -2.68                                                                             47.40                                      8  .800                                                                              11.39                                                                             95.95                                                                             8.12                                                                              77.01                                                                             3.03                                                                              60.52                                                                             .00 .00                                        __________________________________________________________________________     Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.87, K.sub.aR     /γ.sub.aR = 1.25                                                   

The calculation results of the rate of change of K_(a) with respect toγ_(a) at the infinity in-focus arrangement and the closest in-focusarrangement at the wide-angle end, middle position, and telephoto end inthe embodiment of Japanese Patent Application Laid-Open No. 5-142475 andin the fourth embodiment of the present invention are as follows.

    ______________________________________                                        Embodiment of Japanese Patent Application Laid-Open No. 5-142475                        Infinity Arrangement                                                                      Closest Arrangement                                               K.sub.aO /γ.sub.aO                                                                  K.sub.aR /γ.sub.aR                                ______________________________________                                        Wide-angle End                                                                            2.75          0.44                                                (F = 36.0)                                                                    Middle Position                                                                           3.36          0.43                                                (F = 50.0)                                                                    Telephoto End                                                                             3.80          0.43                                                (F = 103.0)                                                                   Fourth Embodiment                                                             Wide-angle End                                                                            0.80          1.28                                                (F = 28.8)                                                                    Middle Position                                                                           0.79          1.30                                                (F = 70.0)                                                                    Telephoto End                                                                             0.87          1.25                                                (F = 133.0)                                                                   ______________________________________                                    

As described above, in the fourth embodiment as well, since the rate ofchange of K_(a) with respect to γ_(a) is small as compared to theconventional system, the contribution of the correction term (ΔBf/μ) inK_(a) =γ_(a) (1-ΔBf/μ) can be reduced. For this reason, an error of theconversion coefficient K_(a) calculated based on γ_(a) and μ or an errorfrom the actual lens driving amount Δa obtained when only one pair of aconversion coefficient γ_(a) value and a correction coefficient μ valueare set can be reduced.

Next, in the embodiment of Japanese Patent Application Laid-Open No.5-142475 and the fourth embodiment of the present invention, when thelens driving amounts upon focusing from the infinity in-focus lensarrangement to the closest distance object and upon focusing from theclosest in-focus lens arrangement to the infinity object at thewide-angle end, middle position, and telephoto end are calculated fromΔa=ΔBf/ γ_(a) (1-ΔBf/μ)!, and errors from the actual lens drivingamounts are then calculated, the following values are obtained. Notethat the value of the correction coefficient μ upon focusing from theinfinity in-focus lens arrangement to the closest distance object adoptsa value at the object distance (POS-5), and the value of the correctioncoefficient μ upon focusing from the closest in-focus lens arrangementto the infinity object adopts a value at the object distance (POS-4).

    ______________________________________                                        Embodiment of Japanese Patent Application Laid-Open No. 5-142475                       Infinity Arrangement →                                                              Closest Arrangement →                                     Closest In-focus State                                                                     Infinity In-focus State                                 ______________________________________                                        Wide-angle End                                                                           -4.4%          -13.0%                                              (F = 36.0)                                                                    Middle Position                                                                          -11.8%         -12.0%                                              (F = 50.0)                                                                    Telephoto End                                                                            -12.6%         -14.6%                                              (F = 103.0)                                                                   Fourth Embodiment                                                             Wide-angle End                                                                           -2.1%          0.2%                                                (F = 28.8)                                                                    Middle Position                                                                          -1.8%          -0.4%                                               (F = 70.0)                                                                    Telephoto End                                                                            0.0%           -0.1%                                               (F = 133.0)                                                                   ______________________________________                                    

As described above, in the fourth embodiment as well, even when only apair of a conversion coefficient γ_(a) value and a correctioncoefficient μ value are set for a given lens arrangement range, an errorbetween the conversion coefficient K_(a) calculated from γ_(a) and μ andthe lens driving amount Δa for focusing becomes small as compared to theconventional system, and focusing can be realized with higher accuracy.

Table 45 summarizes the amount (ANGLE DA) of rotation for focusing uponmanual focusing using the focus cam (the middle table in Table 37) ofthe fourth embodiment, the amount DX (mm) of movement, in the directionof the optical axis, of the focusing lens unit corresponding to theamount of rotation for focusing, and the displacement amount Bf (mm) ofthe imaging point when the amount (DX) of movement in the direction ofthe optical axis is given.

Note that the arrangement of the table and reference symbols are thesame as those in the first embodiment. The upper table in Table 45summarizes the displacement amount (Bf) of the imaging pointcorresponding to the photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.0,and 0.80 m) in the respective zooming states of the focal lengths(F=28.8, 35.0, 50.0, 70.0, 105.0, and 133.0 mm), and the middle tablesummarizes the values of the amount (ANGLE DA) of rotation for focusingrequired for attaining an optimal in-focus state with respect to therespective photographing distances. The lower table summarizes theamounts (DX) of movement, in the direction of the optical axis, of therespective lens units corresponding to the amount (ANGLE DA) of rotationfor focusing in association with the focal lengths and photographingdistances.

                  TABLE 45                                                        ______________________________________                                        Displacement Amount Bf (mm) of Imaging Point and Amount DX                    (mm) of movement for focusing in Fourth Embodiment                                     0.80 m  1.00 m  1.50 m                                                                              2.00 m                                                                              3.00 m                                                                              5.00 m                             ______________________________________                                         28.800 Bf                                                                             .000    .000     .000  .000  .000  .000                               35.000 Bf                                                                             .000    .002     .006  .008  .008  .005                               50.000 Bf                                                                             .000    .009    -.001 -.005 -.007 -.005                               70.000 Bf                                                                             .000    -.021   -.022 -.016 -.011 -.006                              105.000 Bf                                                                             .000    .000    -.009 -.008 -.005 -.006                              133.000 Bf                                                                             .000    .000     .000  .000  .000  .000                              ANGLE DA -5.500  -4.021  -2.409                                                                              -1.721                                                                              -1.096                                                                              -.635                              ______________________________________                                        F     28.800 DX                                                                              .000   1.212 .000 .000 .000 R                                                                              0.80 m                            F     35.000 DX                                                                              .000   1.427 .000 .000 .000 R                                                                              0.80 m                            F     50.000 DX                                                                              .000   1.961 .000 .000 .000 R                                                                              0.80 m                            F     70.000 DX                                                                              .000   2.789 .000 .000 .000 R                                                                              0.80 m                            F    105.000 DX                                                                              .000   4.868 .000 .000 .000 R                                                                              0.80 m                            F    133.000 DX                                                                              .000   6.646 .000 .000 .000 R                                                                              0.80 m                            F     28.800 DX                                                                              .000   .952  .000 .000 .000 R                                                                              1.00 m                            F     35.000 DX                                                                              .000   1.124 .000 .000 .000 R                                                                              1.00 m                            F     50.000 DX                                                                              .000   1.557 .000 .000 .000 R                                                                              1.00 m                            F     70.000 DX                                                                              .000   2.263 .000 .000 .000 R                                                                              1.00 m                            F    105.000 DX                                                                              .000   4.071 .000 .000 .000 R                                                                              1.00 m                            F    133.000 DX                                                                              .000   5.702 .000 .000 .000 R                                                                              1.00 m                            F     28.800 DX                                                                              .000   .621  .000 .000 .000 R                                                                              1.50 m                            F     35.000 DX                                                                              .000   .733  .000 .000 .000 R                                                                              1.50 m                            F     50.000 DX                                                                              .000   1.037 .000 .000 .000 R                                                                              1.50 m                            F     70.000 DX                                                                              .000   1.537 .000 .000 .000 R                                                                              1.50 m                            F    105.000 DX                                                                              .000   2.917 .000 .000 .000 R                                                                              1.50 m                            F    133.000 DX                                                                              .000   4.271 .000 .000 .000 R                                                                              1.50 m                            F     28.800 DX                                                                              .000   .461  .000 .000 .000 R                                                                              2.00 m                            F     35.000 DX                                                                              .000   .542  .000 .000 .000 R                                                                              2.00 m                            F     50.000 DX                                                                              .000   .780  .000 .000 .000 R                                                                              2.00 m                            F     70.000 DX                                                                              .000   1.164 .000 .000 .000 R                                                                              2.00 m                            F    105.000 DX                                                                              .000   2.283 .000 .000 .000 R                                                                              2.00 m                            F    133.000 DX                                                                              .000   3.446 .000 .000 .000 R                                                                              2.00 m                            F     28.800 DX                                                                              .000   .304  .000 .000 .000 R                                                                              3.00 m                            F     35.000 DX                                                                              .000   .356  .000 .000 .000 R                                                                              3.00 m                            F     50.000 DX                                                                              .000   .521  .000 .000 .000 R                                                                              3.00 m                            F     70.000 DX                                                                              .000   .784  .000 .000 .000 R                                                                              3.00 m                            F    105.000 DX                                                                              .000   1.597 .000 .000 .000 R                                                                              3.00 m                            F    133.000 DX                                                                              .000   2.508 .000 .000 .000 R                                                                              3.00 m                            F     28.800 DX                                                                              .000   .181  .000 .000 .000 R                                                                              5.00 m                            F     35.000 DX                                                                              .000   .212  .000 .000 .000 R                                                                              5.00 m                            F     50.000 DX                                                                              .000   .313  .000 .000 .000 R                                                                              5.00 m                            F     70.000 DX                                                                              .000   .475  .000 .000 .000 R                                                                              5.00 m                            F    105.000 DX                                                                              .000   1.002 .000 .000 .000 R                                                                              5.00 m                            F    133.000 DX                                                                              .000   1.640 .000 .000 .000 R                                                                              5.00 m                            ______________________________________                                    

As can be seen from Table 45, so-called manual focusing can be attainedsince the displacement amounts of the imaging point at the respectivefocal lengths and photographing distances are very small, and fallwithin the depth of focus independently of the zooming state andphotographing distance.

As described above in the embodiments, the present invention can beapplied to zoom lens systems based on various lens unit arrangements orfocusing lens units.

As described above, according to the present invention, in an innerfocusing type zoom lens which is attached to, e.g., an auto-focusingcamera which has focus detection means, storage means, calculationmeans, and the like, the number of data of specific coefficients (e.g.,the conversion coefficient γ_(a) and the correction coefficient μ)required for auto-focusing can be reduced as compared to theconventional system. Furthermore, an error upon calculation of the lensdriving amount of the focusing lens unit using the stored specificcoefficients in correspondence with the detected defocus amount can bereduced as compared to the conventional system.

In other words, when the arrangement of the present invention isadopted, since the rate of change of the conversion coefficient γ_(a) isreduced as compared to the conventional system, the number of data ofthe conversion coefficient γ_(a), the correction coefficient μ, and thelike which are stored for calculating the lens driving amount forfocusing can be reduced, and a cost reduction can be realized in termsof the storage capacity.

Furthermore, since the change in conversion coefficient K_(a) to theconversion coefficient γ_(a) becomes small, the contribution of thecorrection term (ΔBf/μ) in K_(a) =γ_(a) (1-ΔBf/μ) can be reduced.

Therefore, an error of the conversion coefficient K_(a) calculated basedon γ_(a) and μ or an error from the actual lens driving amount Δaobtained when only one pair of a conversion coefficient γ_(a) value anda correction coefficient μ value are set for a certain lens arrangementrange can be reduced.

In the present invention, the conversion coefficient γ_(a) at anin-focus point and the conversion coefficient μ which is defined byformula K_(a) =γ_(a) (1-ΔBf/μ) are set to be specific coefficients.Alternatively, a correction coefficient defined by a formula differentfrom the above-mentioned formula may be set. Furthermore, the conversioncoefficient γ_(a) need not always be set in correspondence with thesensitivity (dBf/da) associated with the direction of rotation at anin-focus point. As long as focusing accuracy can be improved, thesensitivity at a point other than the in-focus point and thecorresponding correction coefficient may be set to be specificcoefficients.

Note that the present invention can be applied to various other zoomlens systems based on lens unit arrangements or focusing lens unitsother than those in the above-mentioned embodiments, as a matter ofcourse.

What is claimed is:
 1. A zoom lens system in which a movement locus of afocusing lens unit is defined by synthesizing a focus cam and a zoomcompensation cam so as to achieve an in-focus state by a substantiallyconstant amount of rotation for an identical object distanceindependently of a zooming state upon expression of a predeterminedmovement locus for zooming by an amount of movement, in a direction ofan optical axis, of lens units, and an angle of rotation of a rotatablelens barrel, said zoom lens satisfying the following conditionalformulas at least at the telephoto end:

    1.00<γ.sub.xR /γ.sub.xO

    4.00<Δx.sub.TR /Δ.sub.WR <6.00

    -0.70<a.sub.F /a.sub.Z <-0.50

where γ_(xO) : the ratio (dBf/dx) of an amount dBf of infinitesimalmovement of an imaging plane to an amount dx of infinitesimal movement,in the direction of the optical axis, of said focusing lens unit at aninfinity in-focus point γ_(xR) : the ratio (dBf/dx) of an amount dBf ofinfinitesimal movement of an imaging plane to an amount dx ofinfinitesimal movement, in the direction of the optical axis, of saidfocusing lens unit at a closest in-focus point ΔX_(WR) : an amount ofmovement, in the direction of the optical axis, of said focusing lensunit required for focusing from an infinity position to a closestdistance position at a wide-angle end Δx_(TR) : an amount of movement,in the direction of the optical axis, of said focusing lens unitrequired for focusing from an infinity position to a closest distanceposition at a telephoto end a_(Z) : an amount of rotation of saidfocusing lens unit on said focus cam corresponding to zooming from thewide-angle end to the telephoto end a_(F) : an amount of rotationcorresponding to focusing from an infinity in-focus state to a closestin-focus state.
 2. A zoom lens system according to claim 1, wherein saidzoom lens satisfies the following conditional formula at least at thewide-angle end and the telephoto end:

    0.25<γ.sub.aR /γ.sub.aO <0.75

where γ_(aO) : the ratio (dBf/da) of the amount dBf of infinitesimalmovement of the imaging plane to an amount da of infinitesimal movement,in a direction of rotation, of said focusing lens unit on said focus camat the infinity in-focus point γ_(aR) : the ratio (dBf/da) of the amountdBf of infinitesimal movement of the imaging plane to an amount da ofinfinitesimal movement, in a direction of rotation, of said focusinglens unit on said focus cam at the closest in-focus point.
 3. A zoomlens system according to claim 2, wherein said zoom lens satisfies thefollowing conditional formulas at least at the wide-angle end and thetelephoto end:

    0.60<K.sub.aO /γ.sub.aO <1.20

    0.80<K.sub.aR /γ.sub.aR <1.70

where K_(aO) : the conversion coefficient K_(a), which is expressed byK_(a) =ΔBf/Δa and is obtained when said focusing lens unit is located inlens arrangements corresponding to the infinity in-focus state K_(aR) :the conversion coefficient K_(a), which is expressed by K_(a) =ΔBf/66 aand is obtained when said focusing lens unit is located in lensarrangements corresponding to the closest in-focus state ΔBf: a defocusamount between an imaging position of an object at an arbitrary positionand a predetermined imaging point position Δa: an angle of rotation ofsaid focusing lens unit on said focus cam required for attaining anin-focus state on the object.
 4. A zoom lens system according to claim1, wherein said zoom lens satisfies the following conditional formulasat least at the wide-angle end and the telephoto end:

    0.60<K.sub.aO /γ.sub.aO <1.20

    0.80<K.sub.aR /γ.sub.aR <1.70

where γ_(aO) : the ratio (dBf/da) of the amount dBf of infinitesimalmovement of the imaging plane to an amount da of infinitesimal movement,in a direction of rotation, of said focusing lens unit on said focus camat the infinity in-focus point γ_(aR) : the ratio (dBf/da) of the amountdBf of infinitesimal movement of the imaging plane to an amount da ofinfinitesimal movement, in a direction of rotation, of said focusinglens unit on said focus cam at the closest in-focus point K_(aO) : theconversion coefficient K_(a), which is expressed by K_(a) =ΔBf/Δa and isobtained when said focusing lens unit is located in lens arrangementscorresponding to the infinity in-focus state K_(aR) : the conversioncoefficient K_(a), which is expressed by K_(a) =ΔBf/Δa and is obtainedwhen said focusing lens unit is located in lens arrangementscorresponding to the closest in-focus state ΔBf: a defocus amountbetween an imaging position of an object at an arbitrary position and apredetermined imaging point position Δa: an angle of rotation of saidfocusing lens unit on said focus cam required for attaining an in-focusstate on the object.